id	sid	tid	token	lemma	pos
bracis-33554	1	1	a	a	DET
bracis-33554	1	2	unified	unify	VERB
bracis-33554	1	3	framework	framework	NOUN
bracis-33554	1	4	for	for	ADP
bracis-33554	1	5	average	average	ADJ
bracis-33554	1	6	reward	reward	NOUN
bracis-33554	1	7	criterion	criterion	NOUN
bracis-33554	1	8	and	and	CCONJ
bracis-33554	1	9	risk	risk	NOUN
bracis-33554	1	10	|	|	NOUN
bracis-33554	1	11	springer	springer	NOUN
bracis-33554	1	12	nature	nature	NOUN
bracis-33554	1	13	link	link	PROPN
bracis-33554	1	14	(	(	PUNCT
bracis-33554	1	15	formerly	formerly	ADV
bracis-33554	1	16	springerlink	springerlink	NOUN
bracis-33554	1	17	)	)	PUNCT
bracis-33554	1	18	skip	skip	VERB
bracis-33554	1	19	to	to	ADP
bracis-33554	1	20	main	main	ADJ
bracis-33554	1	21	content	content	NOUN
bracis-33554	1	22	advertisement	advertisement	NOUN
bracis-33554	1	23	log	log	NOUN
bracis-33554	1	24	in	in	ADP
bracis-33554	1	25	menu	menu	NOUN
bracis-33554	1	26	find	find	VERB
bracis-33554	1	27	a	a	DET
bracis-33554	1	28	journal	journal	NOUN
bracis-33554	1	29	publish	publish	VERB
bracis-33554	1	30	with	with	ADP
bracis-33554	1	31	us	we	PRON
bracis-33554	1	32	track	track	VERB
bracis-33554	1	33	your	your	PRON
bracis-33554	1	34	research	research	NOUN
bracis-33554	1	35	search	search	NOUN
bracis-33554	1	36	cart	cart	NOUN
bracis-33554	1	37	home	home	NOUN
bracis-33554	1	38	intelligent	intelligent	ADJ
bracis-33554	1	39	systems	system	NOUN
bracis-33554	1	40	conference	conference	NOUN
bracis-33554	1	41	paper	paper	NOUN
bracis-33554	1	42	a	a	DET
bracis-33554	1	43	unified	unified	ADJ
bracis-33554	1	44	framework	framework	NOUN
bracis-33554	1	45	for	for	ADP
bracis-33554	1	46	average	average	ADJ
bracis-33554	1	47	reward	reward	NOUN
bracis-33554	1	48	criterion	criterion	NOUN
bracis-33554	1	49	and	and	CCONJ
bracis-33554	1	50	risk	risk	NOUN
bracis-33554	1	51	conference	conference	NOUN
bracis-33554	1	52	paper	paper	NOUN
bracis-33554	1	53	first	first	ADV
bracis-33554	1	54	online	online	ADV
bracis-33554	1	55	:	:	PUNCT
bracis-33554	1	56	30	30	NUM
bracis-33554	1	57	january	january	NOUN
bracis-33554	1	58	2025	2025	NUM
bracis-33554	1	59	pp	pp	ADP
bracis-33554	1	60	96–110	96–110	PROPN
bracis-33554	1	61	cite	cite	VERB
bracis-33554	1	62	this	this	DET
bracis-33554	1	63	conference	conference	NOUN
bracis-33554	1	64	paper	paper	NOUN
bracis-33554	1	65	access	access	NOUN
bracis-33554	1	66	provided	provide	VERB
bracis-33554	1	67	by	by	ADP
bracis-33554	1	68	university	university	PROPN
bracis-33554	1	69	of	of	ADP
bracis-33554	1	70	notre	notre	PROPN
bracis-33554	1	71	dame	dame	PROPN
bracis-33554	1	72	hesburgh	hesburgh	PROPN
bracis-33554	1	73	library	library	PROPN
bracis-33554	1	74	download	download	PROPN
bracis-33554	1	75	book	book	NOUN
bracis-33554	1	76	pdf	pdf	PROPN
bracis-33554	1	77	download	download	NOUN
bracis-33554	1	78	book	book	NOUN
bracis-33554	1	79	epub	epub	PROPN
bracis-33554	1	80	intelligent	intelligent	ADJ
bracis-33554	1	81	systems	system	NOUN
bracis-33554	1	82	(	(	PUNCT
bracis-33554	1	83	bracis	bracis	NOUN
bracis-33554	1	84	2024	2024	NUM
bracis-33554	1	85	)	)	PUNCT
bracis-33554	1	86	a	a	DET
bracis-33554	1	87	unified	unified	ADJ
bracis-33554	1	88	framework	framework	NOUN
bracis-33554	1	89	for	for	ADP
bracis-33554	1	90	average	average	ADJ
bracis-33554	1	91	reward	reward	NOUN
bracis-33554	1	92	criterion	criterion	NOUN
bracis-33554	1	93	and	and	CCONJ
bracis-33554	1	94	risk	risk	NOUN
bracis-33554	1	95	download	download	NOUN
bracis-33554	1	96	book	book	NOUN
bracis-33554	1	97	pdf	pdf	PROPN
bracis-33554	1	98	download	download	NOUN
bracis-33554	1	99	book	book	PROPN
bracis-33554	1	100	epub	epub	PROPN
bracis-33554	1	101	willy	willy	PROPN
bracis-33554	1	102	arthur	arthur	PROPN
bracis-33554	1	103	silva	silva	PROPN
bracis-33554	1	104	reis	reis	PROPN
bracis-33554	1	105	  	  	SPACE
bracis-33554	1	106	orcid	orcid	PROPN
bracis-33554	1	107	:	:	PUNCT
bracis-33554	1	108	orcid.org/0000-0002-2621-77139	orcid.org/0000-0002-2621-77139	PROPN
bracis-33554	1	109	,	,	PUNCT
bracis-33554	1	110	karina	karina	PROPN
bracis-33554	1	111	valdivia	valdivia	PROPN
bracis-33554	1	112	delgado	delgado	PROPN
bracis-33554	1	113	  	  	SPACE
bracis-33554	1	114	orcid	orcid	PROPN
bracis-33554	1	115	:	:	PUNCT
bracis-33554	1	116	orcid.org/0000-0002-9120-89879	orcid.org/0000-0002-9120-89879	PROPN
bracis-33554	1	117	&	&	CCONJ
bracis-33554	1	118	valdinei	valdinei	PROPN
bracis-33554	1	119	freire	freire	PROPN
bracis-33554	1	120	  	  	SPACE
bracis-33554	1	121	orcid	orcid	NOUN
bracis-33554	1	122	:	:	PUNCT
bracis-33554	1	123	orcid.org/0000-0003-0330-39319	orcid.org/0000-0003-0330-39319	PROPN
bracis-33554	1	124	  	  	SPACE
bracis-33554	1	125	part	part	NOUN
bracis-33554	1	126	of	of	ADP
bracis-33554	1	127	the	the	DET
bracis-33554	1	128	book	book	NOUN
bracis-33554	1	129	series	series	NOUN
bracis-33554	1	130	:	:	PUNCT
bracis-33554	1	131	lecture	lecture	NOUN
bracis-33554	1	132	notes	note	NOUN
bracis-33554	1	133	in	in	ADP
bracis-33554	1	134	computer	computer	NOUN
bracis-33554	1	135	science	science	NOUN
bracis-33554	1	136	(	(	PUNCT
bracis-33554	1	137	(	(	PUNCT
bracis-33554	1	138	lnai	lnai	ADJ
bracis-33554	1	139	,	,	PUNCT
bracis-33554	1	140	volume	volume	NOUN
bracis-33554	1	141	15412	15412	NUM
bracis-33554	1	142	)	)	PUNCT
bracis-33554	1	143	)	)	PUNCT
bracis-33554	1	144	included	include	VERB
bracis-33554	1	145	in	in	ADP
bracis-33554	1	146	the	the	DET
bracis-33554	1	147	following	follow	VERB
bracis-33554	1	148	conference	conference	NOUN
bracis-33554	1	149	series	series	NOUN
bracis-33554	1	150	:	:	PUNCT
bracis-33554	1	151	brazilian	brazilian	ADJ
bracis-33554	1	152	conference	conference	NOUN
bracis-33554	1	153	on	on	ADP
bracis-33554	1	154	intelligent	intelligent	ADJ
bracis-33554	1	155	systems	system	NOUN
bracis-33554	1	156	497	497	NUM
bracis-33554	1	157	accesses	access	NOUN
bracis-33554	1	158	abstract	abstract	VERB
bracis-33554	1	159	the	the	DET
bracis-33554	1	160	average	average	ADJ
bracis-33554	1	161	reward	reward	NOUN
bracis-33554	1	162	criterion	criterion	NOUN
bracis-33554	1	163	is	be	AUX
bracis-33554	1	164	used	use	VERB
bracis-33554	1	165	to	to	PART
bracis-33554	1	166	solve	solve	VERB
bracis-33554	1	167	infinite	infinite	NOUN
bracis-33554	1	168	-	-	PUNCT
bracis-33554	1	169	horizon	horizon	NOUN
bracis-33554	1	170	mdps	mdps	NOUN
bracis-33554	1	171	.	.	PUNCT
bracis-33554	2	1	this	this	DET
bracis-33554	2	2	risk	risk	NOUN
bracis-33554	2	3	-	-	PUNCT
bracis-33554	2	4	neutral	neutral	ADJ
bracis-33554	2	5	criterion	criterion	NOUN
bracis-33554	2	6	depends	depend	VERB
bracis-33554	2	7	on	on	ADP
bracis-33554	2	8	the	the	DET
bracis-33554	2	9	stochastic	stochastic	ADJ
bracis-33554	2	10	process	process	NOUN
bracis-33554	2	11	in	in	ADP
bracis-33554	2	12	the	the	DET
bracis-33554	2	13	limit	limit	NOUN
bracis-33554	2	14	and	and	CCONJ
bracis-33554	2	15	can	can	AUX
bracis-33554	2	16	use	use	VERB
bracis-33554	2	17	(	(	PUNCT
bracis-33554	2	18	i	i	NOUN
bracis-33554	2	19	)	)	PUNCT
bracis-33554	2	20	the	the	DET
bracis-33554	2	21	accumulated	accumulate	VERB
bracis-33554	2	22	reward	reward	NOUN
bracis-33554	2	23	at	at	ADP
bracis-33554	2	24	infinity	infinity	NOUN
bracis-33554	2	25	,	,	PUNCT
bracis-33554	2	26	which	which	PRON
bracis-33554	2	27	considers	consider	VERB
bracis-33554	2	28	sequences	sequence	NOUN
bracis-33554	2	29	of	of	ADP
bracis-33554	2	30	states	state	NOUN
bracis-33554	2	31	of	of	ADP
bracis-33554	2	32	size	size	NOUN
bracis-33554	2	33	\(h=\infty	\(h=\infty	PROPN
bracis-33554	2	34	\	\	NOUN
bracis-33554	2	35	)	)	PUNCT
bracis-33554	2	36	,	,	PUNCT
bracis-33554	2	37	or	or	CCONJ
bracis-33554	2	38	(	(	PUNCT
bracis-33554	2	39	ii	ii	NOUN
bracis-33554	2	40	)	)	PUNCT
bracis-33554	2	41	the	the	DET
bracis-33554	2	42	steady	steady	ADJ
bracis-33554	2	43	state	state	NOUN
bracis-33554	2	44	distribution	distribution	NOUN
bracis-33554	2	45	of	of	ADP
bracis-33554	2	46	the	the	DET
bracis-33554	2	47	mdp	mdp	NOUN
bracis-33554	2	48	(	(	PUNCT
bracis-33554	2	49	i.e.	i.e.	X
bracis-33554	2	50	,	,	PUNCT
bracis-33554	2	51	the	the	DET
bracis-33554	2	52	probability	probability	NOUN
bracis-33554	2	53	that	that	SCONJ
bracis-33554	2	54	the	the	DET
bracis-33554	2	55	system	system	NOUN
bracis-33554	2	56	is	be	AUX
bracis-33554	2	57	in	in	ADP
bracis-33554	2	58	each	each	DET
bracis-33554	2	59	state	state	NOUN
bracis-33554	2	60	in	in	ADP
bracis-33554	2	61	the	the	DET
bracis-33554	2	62	long	long	ADJ
bracis-33554	2	63	term	term	NOUN
bracis-33554	2	64	)	)	PUNCT
bracis-33554	2	65	,	,	PUNCT
bracis-33554	2	66	which	which	PRON
bracis-33554	2	67	considers	consider	VERB
bracis-33554	2	68	sequences	sequence	NOUN
bracis-33554	2	69	of	of	ADP
bracis-33554	2	70	states	state	NOUN
bracis-33554	2	71	of	of	ADP
bracis-33554	2	72	size	size	NOUN
bracis-33554	2	73	\(h=1\	\(h=1\	PROPN
bracis-33554	2	74	)	)	PUNCT
bracis-33554	2	75	.	.	PUNCT
bracis-33554	3	1	in	in	ADP
bracis-33554	3	2	many	many	ADJ
bracis-33554	3	3	situations	situation	NOUN
bracis-33554	3	4	,	,	PUNCT
bracis-33554	3	5	it	it	PRON
bracis-33554	3	6	is	be	AUX
bracis-33554	3	7	desirable	desirable	ADJ
bracis-33554	3	8	to	to	PART
bracis-33554	3	9	consider	consider	VERB
bracis-33554	3	10	risk	risk	NOUN
bracis-33554	3	11	during	during	ADP
bracis-33554	3	12	the	the	DET
bracis-33554	3	13	process	process	NOUN
bracis-33554	3	14	at	at	ADP
bracis-33554	3	15	each	each	DET
bracis-33554	3	16	stage	stage	NOUN
bracis-33554	3	17	,	,	PUNCT
bracis-33554	3	18	which	which	PRON
bracis-33554	3	19	can	can	AUX
bracis-33554	3	20	be	be	AUX
bracis-33554	3	21	achieved	achieve	VERB
bracis-33554	3	22	with	with	ADP
bracis-33554	3	23	the	the	DET
bracis-33554	3	24	average	average	ADJ
bracis-33554	3	25	reward	reward	NOUN
bracis-33554	3	26	criterion	criterion	NOUN
bracis-33554	3	27	using	use	VERB
bracis-33554	3	28	a	a	DET
bracis-33554	3	29	utility	utility	NOUN
bracis-33554	3	30	function	function	NOUN
bracis-33554	3	31	or	or	CCONJ
bracis-33554	3	32	a	a	DET
bracis-33554	3	33	risk	risk	NOUN
bracis-33554	3	34	measure	measure	NOUN
bracis-33554	3	35	such	such	ADJ
bracis-33554	3	36	as	as	ADP
bracis-33554	3	37	var	var	NOUN
bracis-33554	3	38	and	and	CCONJ
bracis-33554	3	39	cvar	cvar	NOUN
bracis-33554	3	40	.	.	PUNCT
bracis-33554	4	1	the	the	DET
bracis-33554	4	2	objective	objective	NOUN
bracis-33554	4	3	of	of	ADP
bracis-33554	4	4	this	this	DET
bracis-33554	4	5	work	work	NOUN
bracis-33554	4	6	is	be	AUX
bracis-33554	4	7	to	to	PART
bracis-33554	4	8	propose	propose	VERB
bracis-33554	4	9	a	a	DET
bracis-33554	4	10	mathematical	mathematical	ADJ
bracis-33554	4	11	framework	framework	NOUN
bracis-33554	4	12	that	that	PRON
bracis-33554	4	13	allows	allow	VERB
bracis-33554	4	14	a	a	DET
bracis-33554	4	15	unified	unified	ADJ
bracis-33554	4	16	treatment	treatment	NOUN
bracis-33554	4	17	of	of	ADP
bracis-33554	4	18	the	the	DET
bracis-33554	4	19	existing	exist	VERB
bracis-33554	4	20	literature	literature	NOUN
bracis-33554	4	21	using	use	VERB
bracis-33554	4	22	average	average	ADJ
bracis-33554	4	23	reward	reward	NOUN
bracis-33554	4	24	and	and	CCONJ
bracis-33554	4	25	risk	risk	NOUN
bracis-33554	4	26	,	,	PUNCT
bracis-33554	4	27	including	include	VERB
bracis-33554	4	28	works	work	NOUN
bracis-33554	4	29	that	that	PRON
bracis-33554	4	30	use	use	VERB
bracis-33554	4	31	exponential	exponential	ADJ
bracis-33554	4	32	utility	utility	NOUN
bracis-33554	4	33	functions	function	NOUN
bracis-33554	4	34	and	and	CCONJ
bracis-33554	4	35	cvar	cvar	NOUN
bracis-33554	4	36	,	,	PUNCT
bracis-33554	4	37	as	as	ADV
bracis-33554	4	38	well	well	ADV
bracis-33554	4	39	as	as	ADP
bracis-33554	4	40	to	to	PART
bracis-33554	4	41	include	include	VERB
bracis-33554	4	42	interpretations	interpretation	NOUN
bracis-33554	4	43	with	with	ADP
bracis-33554	4	44	\(1	\(1	PROPN
bracis-33554	4	45	\le	\le	PROPN
bracis-33554	4	46	h	h	NOUN
bracis-33554	4	47	\le	\le	PROPN
bracis-33554	4	48	\infty	\infty	PROPN
bracis-33554	4	49	\	\	PROPN
bracis-33554	4	50	)	)	PUNCT
bracis-33554	4	51	not	not	PART
bracis-33554	4	52	present	present	ADJ
bracis-33554	4	53	in	in	ADP
bracis-33554	4	54	the	the	DET
bracis-33554	4	55	literature	literature	NOUN
bracis-33554	4	56	.	.	PUNCT
bracis-33554	5	1	these	these	DET
bracis-33554	5	2	new	new	ADJ
bracis-33554	5	3	interpretations	interpretation	NOUN
bracis-33554	5	4	allow	allow	VERB
bracis-33554	5	5	differentiating	differentiate	VERB
bracis-33554	5	6	policies	policy	NOUN
bracis-33554	5	7	that	that	PRON
bracis-33554	5	8	may	may	AUX
bracis-33554	5	9	not	not	PART
bracis-33554	5	10	be	be	AUX
bracis-33554	5	11	distinguished	distinguish	VERB
bracis-33554	5	12	from	from	ADP
bracis-33554	5	13	existing	exist	VERB
bracis-33554	5	14	criteria	criterion	NOUN
bracis-33554	5	15	.	.	PUNCT
bracis-33554	6	1	a	a	DET
bracis-33554	6	2	numerical	numerical	ADJ
bracis-33554	6	3	example	example	NOUN
bracis-33554	6	4	shows	show	VERB
bracis-33554	6	5	the	the	DET
bracis-33554	6	6	behaviors	behavior	NOUN
bracis-33554	6	7	of	of	ADP
bracis-33554	6	8	the	the	DET
bracis-33554	6	9	criteria	criterion	NOUN
bracis-33554	6	10	considering	consider	VERB
bracis-33554	6	11	this	this	DET
bracis-33554	6	12	new	new	ADJ
bracis-33554	6	13	framework	framework	NOUN
bracis-33554	6	14	.	.	PUNCT
bracis-33554	7	1	access	access	NOUN
bracis-33554	7	2	provided	provide	VERB
bracis-33554	7	3	by	by	ADP
bracis-33554	7	4	university	university	PROPN
bracis-33554	7	5	of	of	ADP
bracis-33554	7	6	notre	notre	PROPN
bracis-33554	7	7	dame	dame	PROPN
bracis-33554	7	8	hesburgh	hesburgh	PROPN
bracis-33554	7	9	library	library	PROPN
bracis-33554	7	10	.	.	PUNCT
bracis-33554	8	1	download	download	PROPN
bracis-33554	8	2	conference	conference	NOUN
bracis-33554	8	3	paper	paper	NOUN
bracis-33554	8	4	pdf	pdf	NOUN
bracis-33554	8	5	similar	similar	ADJ
bracis-33554	8	6	content	content	NOUN
bracis-33554	8	7	being	be	AUX
bracis-33554	8	8	viewed	view	VERB
bracis-33554	8	9	by	by	ADP
bracis-33554	8	10	others	other	NOUN
bracis-33554	8	11	solving	solve	VERB
bracis-33554	8	12	markov	markov	NOUN
bracis-33554	8	13	decision	decision	NOUN
bracis-33554	8	14	processes	process	NOUN
bracis-33554	8	15	with	with	ADP
bracis-33554	8	16	downside	downside	ADJ
bracis-33554	8	17	risk	risk	NOUN
bracis-33554	8	18	adjustment	adjustment	NOUN
bracis-33554	8	19	article	article	NOUN
bracis-33554	8	20	11	11	NUM
bracis-33554	8	21	june	june	PROPN
bracis-33554	8	22	2016	2016	NUM
bracis-33554	8	23	sufficient	sufficient	ADJ
bracis-33554	8	24	stochastic	stochastic	ADJ
bracis-33554	8	25	maximum	maximum	ADJ
bracis-33554	8	26	principle	principle	NOUN
bracis-33554	8	27	for	for	ADP
bracis-33554	8	28	mean	mean	ADJ
bracis-33554	8	29	-	-	PUNCT
bracis-33554	8	30	field	field	NOUN
bracis-33554	8	31	control	control	NOUN
bracis-33554	8	32	problems	problem	NOUN
bracis-33554	8	33	with	with	ADP
bracis-33554	8	34	regime	regime	NOUN
bracis-33554	8	35	switching	switch	VERB
bracis-33554	8	36	in	in	ADP
bracis-33554	8	37	an	an	DET
bracis-33554	8	38	infinite	infinite	ADJ
bracis-33554	8	39	horizon	horizon	NOUN
bracis-33554	8	40	article	article	NOUN
bracis-33554	8	41	05	05	NUM
bracis-33554	8	42	november	november	PROPN
bracis-33554	8	43	2025	2025	NUM
bracis-33554	8	44	revisiting	revisit	VERB
bracis-33554	8	45	the	the	DET
bracis-33554	8	46	merton	merton	ADJ
bracis-33554	8	47	problem	problem	NOUN
bracis-33554	8	48	:	:	PUNCT
bracis-33554	8	49	from	from	ADP
bracis-33554	8	50	hara	hara	PROPN
bracis-33554	8	51	to	to	ADP
bracis-33554	8	52	cara	cara	VERB
bracis-33554	8	53	utility	utility	NOUN
bracis-33554	8	54	article	article	NOUN
bracis-33554	8	55	22	22	NUM
bracis-33554	8	56	february	february	NOUN
bracis-33554	8	57	2021	2021	NUM
bracis-33554	8	58	1	1	NUM
bracis-33554	8	59	introduction	introduction	NOUN
bracis-33554	8	60	a	a	DET
bracis-33554	8	61	markov	markov	NOUN
bracis-33554	8	62	decision	decision	NOUN
bracis-33554	8	63	process	process	NOUN
bracis-33554	8	64	(	(	PUNCT
bracis-33554	8	65	mdp	mdp	NOUN
bracis-33554	8	66	)	)	PUNCT
bracis-33554	8	67	provides	provide	VERB
bracis-33554	8	68	a	a	DET
bracis-33554	8	69	mathematical	mathematical	ADJ
bracis-33554	8	70	framework	framework	NOUN
bracis-33554	8	71	for	for	ADP
bracis-33554	8	72	representing	represent	VERB
bracis-33554	8	73	and	and	CCONJ
bracis-33554	8	74	solving	solve	VERB
bracis-33554	8	75	sequential	sequential	ADJ
bracis-33554	8	76	decision	decision	NOUN
bracis-33554	8	77	-	-	PUNCT
bracis-33554	8	78	making	make	VERB
bracis-33554	8	79	problems	problem	NOUN
bracis-33554	8	80	under	under	ADP
bracis-33554	8	81	uncertainty	uncertainty	NOUN
bracis-33554	8	82	in	in	ADP
bracis-33554	8	83	fully	fully	ADV
bracis-33554	8	84	observable	observable	ADJ
bracis-33554	8	85	environments	environment	NOUN
bracis-33554	8	86	[	[	X
bracis-33554	8	87	4	4	NUM
bracis-33554	8	88	]	]	PUNCT
bracis-33554	8	89	.	.	PUNCT
bracis-33554	9	1	in	in	ADP
bracis-33554	9	2	these	these	DET
bracis-33554	9	3	problems	problem	NOUN
bracis-33554	9	4	,	,	PUNCT
bracis-33554	9	5	an	an	DET
bracis-33554	9	6	agent	agent	NOUN
bracis-33554	9	7	must	must	AUX
bracis-33554	9	8	interact	interact	VERB
bracis-33554	9	9	with	with	ADP
bracis-33554	9	10	an	an	DET
bracis-33554	9	11	environment	environment	NOUN
bracis-33554	9	12	through	through	ADP
bracis-33554	9	13	actions	action	NOUN
bracis-33554	9	14	that	that	PRON
bracis-33554	9	15	can	can	AUX
bracis-33554	9	16	have	have	VERB
bracis-33554	9	17	stochastic	stochastic	ADJ
bracis-33554	9	18	outcomes	outcome	NOUN
bracis-33554	9	19	.	.	PUNCT
bracis-33554	10	1	various	various	ADJ
bracis-33554	10	2	optimization	optimization	NOUN
bracis-33554	10	3	criteria	criterion	NOUN
bracis-33554	10	4	are	be	AUX
bracis-33554	10	5	used	use	VERB
bracis-33554	10	6	to	to	PART
bracis-33554	10	7	find	find	VERB
bracis-33554	10	8	an	an	DET
bracis-33554	10	9	optimal	optimal	ADJ
bracis-33554	10	10	policy	policy	NOUN
bracis-33554	10	11	for	for	ADP
bracis-33554	10	12	a	a	DET
bracis-33554	10	13	markov	markov	NOUN
bracis-33554	10	14	decision	decision	NOUN
bracis-33554	10	15	process	process	NOUN
bracis-33554	10	16	.	.	PUNCT
bracis-33554	11	1	the	the	DET
bracis-33554	11	2	most	most	ADV
bracis-33554	11	3	commonly	commonly	ADV
bracis-33554	11	4	used	use	VERB
bracis-33554	11	5	criterion	criterion	NOUN
bracis-33554	11	6	in	in	ADP
bracis-33554	11	7	finite	finite	ADJ
bracis-33554	11	8	and	and	CCONJ
bracis-33554	11	9	indefinite	indefinite	ADJ
bracis-33554	11	10	horizon	horizon	NOUN
bracis-33554	11	11	mdps	mdps	NOUN
bracis-33554	11	12	is	be	AUX
bracis-33554	11	13	accumulated	accumulate	VERB
bracis-33554	11	14	reward	reward	NOUN
bracis-33554	11	15	.	.	PUNCT
bracis-33554	12	1	in	in	ADP
bracis-33554	12	2	infinite	infinite	ADJ
bracis-33554	12	3	horizon	horizon	NOUN
bracis-33554	12	4	problems	problem	NOUN
bracis-33554	12	5	,	,	PUNCT
bracis-33554	12	6	the	the	DET
bracis-33554	12	7	average	average	ADJ
bracis-33554	12	8	reward	reward	NOUN
bracis-33554	12	9	per	per	ADP
bracis-33554	12	10	decision	decision	NOUN
bracis-33554	12	11	step	step	NOUN
bracis-33554	12	12	criterion	criterion	NOUN
bracis-33554	12	13	is	be	AUX
bracis-33554	12	14	used	use	VERB
bracis-33554	12	15	.	.	PUNCT
bracis-33554	13	1	the	the	DET
bracis-33554	13	2	average	average	ADJ
bracis-33554	13	3	reward	reward	NOUN
bracis-33554	13	4	criterion	criterion	NOUN
bracis-33554	13	5	is	be	AUX
bracis-33554	13	6	also	also	ADV
bracis-33554	13	7	known	know	VERB
bracis-33554	13	8	as	as	ADP
bracis-33554	13	9	long	long	ADV
bracis-33554	13	10	-	-	PUNCT
bracis-33554	13	11	run	run	VERB
bracis-33554	13	12	average	average	ADJ
bracis-33554	13	13	reward	reward	NOUN
bracis-33554	13	14	,	,	PUNCT
bracis-33554	13	15	mean	mean	NOUN
bracis-33554	13	16	-	-	PUNCT
bracis-33554	13	17	payoff	payoff	NOUN
bracis-33554	13	18	,	,	PUNCT
bracis-33554	13	19	limit	limit	NOUN
bracis-33554	13	20	-	-	PUNCT
bracis-33554	13	21	average	average	NOUN
bracis-33554	13	22	reward	reward	NOUN
bracis-33554	13	23	,	,	PUNCT
bracis-33554	13	24	or	or	CCONJ
bracis-33554	13	25	steady	steady	ADJ
bracis-33554	13	26	-	-	PUNCT
bracis-33554	13	27	state	state	NOUN
bracis-33554	13	28	reward	reward	NOUN
bracis-33554	13	29	[	[	X
bracis-33554	13	30	1	1	NUM
bracis-33554	13	31	]	]	PUNCT
bracis-33554	13	32	.	.	PUNCT
bracis-33554	14	1	this	this	DET
bracis-33554	14	2	criterion	criterion	NOUN
bracis-33554	14	3	is	be	AUX
bracis-33554	14	4	risk	risk	NOUN
bracis-33554	14	5	-	-	PUNCT
bracis-33554	14	6	neutral	neutral	ADJ
bracis-33554	14	7	,	,	PUNCT
bracis-33554	14	8	does	do	AUX
bracis-33554	14	9	not	not	PART
bracis-33554	14	10	use	use	VERB
bracis-33554	14	11	discount	discount	NOUN
bracis-33554	14	12	,	,	PUNCT
bracis-33554	14	13	and	and	CCONJ
bracis-33554	14	14	is	be	AUX
bracis-33554	14	15	naturally	naturally	ADV
bracis-33554	14	16	used	use	VERB
bracis-33554	14	17	in	in	ADP
bracis-33554	14	18	cyclic	cyclic	ADJ
bracis-33554	14	19	and	and	CCONJ
bracis-33554	14	20	non	non	ADJ
bracis-33554	14	21	-	-	ADJ
bracis-33554	14	22	terminating	terminating	ADJ
bracis-33554	14	23	problems	problem	NOUN
bracis-33554	14	24	.	.	PUNCT
bracis-33554	15	1	this	this	DET
bracis-33554	15	2	criterion	criterion	NOUN
bracis-33554	15	3	is	be	AUX
bracis-33554	15	4	fundamental	fundamental	ADJ
bracis-33554	15	5	for	for	ADP
bracis-33554	15	6	areas	area	NOUN
bracis-33554	15	7	such	such	ADJ
bracis-33554	15	8	as	as	ADP
bracis-33554	15	9	controlled	control	VERB
bracis-33554	15	10	queues	queue	NOUN
bracis-33554	15	11	and	and	CCONJ
bracis-33554	15	12	inventory	inventory	NOUN
bracis-33554	15	13	systems	system	NOUN
bracis-33554	15	14	with	with	ADP
bracis-33554	15	15	frequent	frequent	ADJ
bracis-33554	15	16	restocking	restocking	NOUN
bracis-33554	15	17	,	,	PUNCT
bracis-33554	15	18	where	where	SCONJ
bracis-33554	15	19	decisions	decision	NOUN
bracis-33554	15	20	are	be	AUX
bracis-33554	15	21	made	make	VERB
bracis-33554	15	22	frequently	frequently	ADV
bracis-33554	15	23	and	and	CCONJ
bracis-33554	15	24	continually	continually	ADV
bracis-33554	15	25	[	[	X
bracis-33554	15	26	4	4	NUM
bracis-33554	15	27	]	]	PUNCT
bracis-33554	15	28	.	.	PUNCT
bracis-33554	16	1	it	it	PRON
bracis-33554	16	2	is	be	AUX
bracis-33554	16	3	also	also	ADV
bracis-33554	16	4	important	important	ADJ
bracis-33554	16	5	for	for	ADP
bracis-33554	16	6	natural	natural	ADJ
bracis-33554	16	7	resource	resource	NOUN
bracis-33554	16	8	management	management	NOUN
bracis-33554	16	9	and	and	CCONJ
bracis-33554	16	10	environmental	environmental	ADJ
bracis-33554	16	11	economics	economic	NOUN
bracis-33554	16	12	,	,	PUNCT
bracis-33554	16	13	for	for	ADP
bracis-33554	16	14	example	example	NOUN
bracis-33554	16	15	,	,	PUNCT
bracis-33554	16	16	to	to	PART
bracis-33554	16	17	determine	determine	VERB
bracis-33554	16	18	the	the	DET
bracis-33554	16	19	extraction	extraction	NOUN
bracis-33554	16	20	rate	rate	NOUN
bracis-33554	16	21	of	of	ADP
bracis-33554	16	22	a	a	DET
bracis-33554	16	23	renewable	renewable	ADJ
bracis-33554	16	24	natural	natural	ADJ
bracis-33554	16	25	resource	resource	NOUN
bracis-33554	16	26	[	[	X
bracis-33554	16	27	3	3	NUM
bracis-33554	16	28	]	]	PUNCT
bracis-33554	16	29	.	.	PUNCT
bracis-33554	17	1	the	the	DET
bracis-33554	17	2	average	average	ADJ
bracis-33554	17	3	reward	reward	NOUN
bracis-33554	17	4	criterion	criterion	NOUN
bracis-33554	17	5	depends	depend	VERB
bracis-33554	17	6	on	on	ADP
bracis-33554	17	7	the	the	DET
bracis-33554	17	8	behavior	behavior	NOUN
bracis-33554	17	9	of	of	ADP
bracis-33554	17	10	the	the	DET
bracis-33554	17	11	stochastic	stochastic	ADJ
bracis-33554	17	12	process	process	NOUN
bracis-33554	17	13	in	in	ADP
bracis-33554	17	14	the	the	DET
bracis-33554	17	15	limit	limit	NOUN
bracis-33554	17	16	,	,	PUNCT
bracis-33554	17	17	which	which	PRON
bracis-33554	17	18	determines	determine	VERB
bracis-33554	17	19	some	some	DET
bracis-33554	17	20	models	model	NOUN
bracis-33554	17	21	of	of	ADP
bracis-33554	17	22	the	the	DET
bracis-33554	17	23	criterion	criterion	NOUN
bracis-33554	17	24	according	accord	VERB
bracis-33554	17	25	to	to	ADP
bracis-33554	17	26	the	the	DET
bracis-33554	17	27	structure	structure	NOUN
bracis-33554	17	28	of	of	ADP
bracis-33554	17	29	the	the	DET
bracis-33554	17	30	markov	markov	NOUN
bracis-33554	17	31	chain	chain	NOUN
bracis-33554	17	32	generated	generate	VERB
bracis-33554	17	33	by	by	ADP
bracis-33554	17	34	stationary	stationary	ADJ
bracis-33554	17	35	policies	policy	NOUN
bracis-33554	17	36	.	.	PUNCT
bracis-33554	18	1	one	one	NUM
bracis-33554	18	2	way	way	NOUN
bracis-33554	18	3	to	to	PART
bracis-33554	18	4	think	think	VERB
bracis-33554	18	5	about	about	ADP
bracis-33554	18	6	the	the	DET
bracis-33554	18	7	stochastic	stochastic	ADJ
bracis-33554	18	8	process	process	NOUN
bracis-33554	18	9	in	in	ADP
bracis-33554	18	10	the	the	DET
bracis-33554	18	11	limit	limit	NOUN
bracis-33554	18	12	is	be	AUX
bracis-33554	18	13	by	by	ADP
bracis-33554	18	14	summing	sum	VERB
bracis-33554	18	15	the	the	DET
bracis-33554	18	16	rewards	reward	NOUN
bracis-33554	18	17	(	(	PUNCT
bracis-33554	18	18	i.e.	i.e.	X
bracis-33554	18	19	,	,	PUNCT
bracis-33554	18	20	calculating	calculate	VERB
bracis-33554	18	21	the	the	DET
bracis-33554	18	22	expected	expect	VERB
bracis-33554	18	23	accumulated	accumulate	VERB
bracis-33554	18	24	reward	reward	NOUN
bracis-33554	18	25	)	)	PUNCT
bracis-33554	18	26	and	and	CCONJ
bracis-33554	18	27	then	then	ADV
bracis-33554	18	28	calculating	calculate	VERB
bracis-33554	18	29	how	how	SCONJ
bracis-33554	18	30	much	much	ADJ
bracis-33554	18	31	is	be	AUX
bracis-33554	18	32	added	add	VERB
bracis-33554	18	33	to	to	ADP
bracis-33554	18	34	this	this	DET
bracis-33554	18	35	sum	sum	NOUN
bracis-33554	18	36	at	at	ADP
bracis-33554	18	37	each	each	DET
bracis-33554	18	38	step	step	NOUN
bracis-33554	18	39	,	,	PUNCT
bracis-33554	18	40	which	which	PRON
bracis-33554	18	41	is	be	AUX
bracis-33554	18	42	called	call	VERB
bracis-33554	18	43	gain	gain	NOUN
bracis-33554	18	44	.	.	PUNCT
bracis-33554	19	1	when	when	SCONJ
bracis-33554	19	2	time	time	NOUN
bracis-33554	19	3	tends	tend	VERB
bracis-33554	19	4	to	to	PART
bracis-33554	19	5	infinity	infinity	VERB
bracis-33554	19	6	,	,	PUNCT
bracis-33554	19	7	the	the	DET
bracis-33554	19	8	gain	gain	NOUN
bracis-33554	19	9	tends	tend	VERB
bracis-33554	19	10	to	to	ADP
bracis-33554	19	11	a	a	DET
bracis-33554	19	12	constant	constant	ADJ
bracis-33554	19	13	value	value	NOUN
bracis-33554	19	14	.	.	PUNCT
bracis-33554	20	1	since	since	SCONJ
bracis-33554	20	2	this	this	DET
bracis-33554	20	3	sum	sum	NOUN
bracis-33554	20	4	considers	consider	VERB
bracis-33554	20	5	sequences	sequence	NOUN
bracis-33554	20	6	of	of	ADP
bracis-33554	20	7	\(h=\infty	\(h=\infty	NUM
bracis-33554	20	8	\	\	NOUN
bracis-33554	20	9	)	)	PUNCT
bracis-33554	20	10	states	state	NOUN
bracis-33554	20	11	,	,	PUNCT
bracis-33554	20	12	this	this	DET
bracis-33554	20	13	way	way	NOUN
bracis-33554	20	14	of	of	ADP
bracis-33554	20	15	thinking	thinking	NOUN
bracis-33554	20	16	in	in	ADP
bracis-33554	20	17	this	this	DET
bracis-33554	20	18	work	work	NOUN
bracis-33554	20	19	is	be	AUX
bracis-33554	20	20	called	call	VERB
bracis-33554	20	21	\(h=\infty	\(h=\infty	PROPN
bracis-33554	20	22	\	\	NOUN
bracis-33554	20	23	)	)	PUNCT
bracis-33554	20	24	.	.	PUNCT
bracis-33554	21	1	another	another	DET
bracis-33554	21	2	way	way	NOUN
bracis-33554	21	3	to	to	PART
bracis-33554	21	4	think	think	VERB
bracis-33554	21	5	about	about	ADP
bracis-33554	21	6	the	the	DET
bracis-33554	21	7	stochastic	stochastic	ADJ
bracis-33554	21	8	process	process	NOUN
bracis-33554	21	9	in	in	ADP
bracis-33554	21	10	the	the	DET
bracis-33554	21	11	limit	limit	NOUN
bracis-33554	21	12	is	be	AUX
bracis-33554	21	13	by	by	ADP
bracis-33554	21	14	calculating	calculate	VERB
bracis-33554	21	15	the	the	DET
bracis-33554	21	16	steady	steady	ADJ
bracis-33554	21	17	-	-	PUNCT
bracis-33554	21	18	state	state	NOUN
bracis-33554	21	19	distribution	distribution	NOUN
bracis-33554	21	20	,	,	PUNCT
bracis-33554	21	21	i.e.	i.e.	X
bracis-33554	21	22	,	,	PUNCT
bracis-33554	21	23	calculating	calculate	VERB
bracis-33554	21	24	the	the	DET
bracis-33554	21	25	probability	probability	NOUN
bracis-33554	21	26	that	that	SCONJ
bracis-33554	21	27	the	the	DET
bracis-33554	21	28	system	system	NOUN
bracis-33554	21	29	is	be	AUX
bracis-33554	21	30	in	in	ADP
bracis-33554	21	31	each	each	DET
bracis-33554	21	32	state	state	NOUN
bracis-33554	21	33	in	in	ADP
bracis-33554	21	34	the	the	DET
bracis-33554	21	35	long	long	ADJ
bracis-33554	21	36	term	term	NOUN
bracis-33554	21	37	.	.	PUNCT
bracis-33554	22	1	considering	consider	VERB
bracis-33554	22	2	these	these	DET
bracis-33554	22	3	probabilities	probability	NOUN
bracis-33554	22	4	and	and	CCONJ
bracis-33554	22	5	the	the	DET
bracis-33554	22	6	immediate	immediate	ADJ
bracis-33554	22	7	reward	reward	NOUN
bracis-33554	22	8	,	,	PUNCT
bracis-33554	22	9	the	the	DET
bracis-33554	22	10	expected	expect	VERB
bracis-33554	22	11	reward	reward	NOUN
bracis-33554	22	12	is	be	AUX
bracis-33554	22	13	calculated	calculate	VERB
bracis-33554	22	14	.	.	PUNCT
bracis-33554	23	1	this	this	DET
bracis-33554	23	2	way	way	NOUN
bracis-33554	23	3	of	of	ADP
bracis-33554	23	4	thinking	thinking	NOUN
bracis-33554	23	5	in	in	ADP
bracis-33554	23	6	this	this	DET
bracis-33554	23	7	work	work	NOUN
bracis-33554	23	8	is	be	AUX
bracis-33554	23	9	called	call	VERB
bracis-33554	23	10	\(h=1\	\(h=1\	PROPN
bracis-33554	23	11	)	)	PUNCT
bracis-33554	23	12	.	.	PUNCT
bracis-33554	24	1	considering	consider	VERB
bracis-33554	24	2	the	the	DET
bracis-33554	24	3	risk	risk	NOUN
bracis-33554	24	4	-	-	PUNCT
bracis-33554	24	5	neutral	neutral	ADJ
bracis-33554	24	6	average	average	ADJ
bracis-33554	24	7	reward	reward	NOUN
bracis-33554	24	8	criterion	criterion	NOUN
bracis-33554	24	9	,	,	PUNCT
bracis-33554	24	10	both	both	DET
bracis-33554	24	11	ways	way	NOUN
bracis-33554	24	12	of	of	ADP
bracis-33554	24	13	thinking	think	VERB
bracis-33554	24	14	about	about	ADP
bracis-33554	24	15	the	the	DET
bracis-33554	24	16	stochastic	stochastic	ADJ
bracis-33554	24	17	process	process	NOUN
bracis-33554	24	18	in	in	ADP
bracis-33554	24	19	the	the	DET
bracis-33554	24	20	limit	limit	NOUN
bracis-33554	24	21	yield	yield	VERB
bracis-33554	24	22	the	the	DET
bracis-33554	24	23	same	same	ADJ
bracis-33554	24	24	result	result	NOUN
bracis-33554	24	25	.	.	PUNCT
bracis-33554	25	1	in	in	ADP
bracis-33554	25	2	many	many	ADJ
bracis-33554	25	3	situations	situation	NOUN
bracis-33554	25	4	,	,	PUNCT
bracis-33554	25	5	it	it	PRON
bracis-33554	25	6	is	be	AUX
bracis-33554	25	7	desirable	desirable	ADJ
bracis-33554	25	8	to	to	PART
bracis-33554	25	9	consider	consider	VERB
bracis-33554	25	10	risk	risk	NOUN
bracis-33554	25	11	during	during	ADP
bracis-33554	25	12	the	the	DET
bracis-33554	25	13	process	process	NOUN
bracis-33554	25	14	at	at	ADP
bracis-33554	25	15	each	each	DET
bracis-33554	25	16	stage	stage	NOUN
bracis-33554	25	17	.	.	PUNCT
bracis-33554	26	1	in	in	ADP
bracis-33554	26	2	the	the	DET
bracis-33554	26	3	financial	financial	ADJ
bracis-33554	26	4	field	field	NOUN
bracis-33554	26	5	,	,	PUNCT
bracis-33554	26	6	for	for	ADP
bracis-33554	26	7	example	example	NOUN
bracis-33554	26	8	,	,	PUNCT
bracis-33554	26	9	a	a	DET
bracis-33554	26	10	risk	risk	NOUN
bracis-33554	26	11	-	-	PUNCT
bracis-33554	26	12	averse	averse	ADJ
bracis-33554	26	13	investor	investor	NOUN
bracis-33554	26	14	might	might	AUX
bracis-33554	26	15	prefer	prefer	VERB
bracis-33554	26	16	to	to	PART
bracis-33554	26	17	minimize	minimize	VERB
bracis-33554	26	18	uncertainties	uncertainty	NOUN
bracis-33554	26	19	by	by	ADP
bracis-33554	26	20	opting	opt	VERB
bracis-33554	26	21	for	for	ADP
bracis-33554	26	22	a	a	DET
bracis-33554	26	23	lower	low	ADJ
bracis-33554	26	24	guaranteed	guarantee	VERB
bracis-33554	26	25	return	return	NOUN
bracis-33554	26	26	,	,	PUNCT
bracis-33554	26	27	even	even	ADV
bracis-33554	26	28	if	if	SCONJ
bracis-33554	26	29	this	this	PRON
bracis-33554	26	30	implies	imply	VERB
bracis-33554	26	31	obtaining	obtain	VERB
bracis-33554	26	32	a	a	DET
bracis-33554	26	33	smaller	small	ADJ
bracis-33554	26	34	gain	gain	NOUN
bracis-33554	26	35	[	[	X
bracis-33554	26	36	7	7	NUM
bracis-33554	26	37	]	]	PUNCT
bracis-33554	26	38	.	.	PUNCT
bracis-33554	27	1	moreover	moreover	ADV
bracis-33554	27	2	,	,	PUNCT
bracis-33554	27	3	considering	consider	VERB
bracis-33554	27	4	risk	risk	NOUN
bracis-33554	27	5	at	at	ADP
bracis-33554	27	6	each	each	DET
bracis-33554	27	7	stage	stage	NOUN
bracis-33554	27	8	can	can	AUX
bracis-33554	27	9	increase	increase	VERB
bracis-33554	27	10	the	the	DET
bracis-33554	27	11	robustness	robustness	NOUN
bracis-33554	27	12	of	of	ADP
bracis-33554	27	13	policies	policy	NOUN
bracis-33554	27	14	,	,	PUNCT
bracis-33554	27	15	allowing	allow	VERB
bracis-33554	27	16	them	they	PRON
bracis-33554	27	17	to	to	PART
bracis-33554	27	18	function	function	VERB
bracis-33554	27	19	in	in	ADP
bracis-33554	27	20	a	a	DET
bracis-33554	27	21	wider	wide	ADJ
bracis-33554	27	22	variety	variety	NOUN
bracis-33554	27	23	of	of	ADP
bracis-33554	27	24	scenarios	scenario	NOUN
bracis-33554	27	25	,	,	PUNCT
bracis-33554	27	26	such	such	ADJ
bracis-33554	27	27	as	as	ADP
bracis-33554	27	28	in	in	ADP
bracis-33554	27	29	the	the	DET
bracis-33554	27	30	use	use	NOUN
bracis-33554	27	31	of	of	ADP
bracis-33554	27	32	renewable	renewable	ADJ
bracis-33554	27	33	natural	natural	ADJ
bracis-33554	27	34	resources	resource	NOUN
bracis-33554	27	35	that	that	PRON
bracis-33554	27	36	suffer	suffer	VERB
bracis-33554	27	37	from	from	ADP
bracis-33554	27	38	greater	great	ADJ
bracis-33554	27	39	volatility	volatility	NOUN
bracis-33554	27	40	due	due	ADP
bracis-33554	27	41	to	to	ADP
bracis-33554	27	42	climate	climate	NOUN
bracis-33554	27	43	change	change	NOUN
bracis-33554	27	44	.	.	PUNCT
bracis-33554	28	1	among	among	ADP
bracis-33554	28	2	the	the	DET
bracis-33554	28	3	works	work	NOUN
bracis-33554	28	4	that	that	PRON
bracis-33554	28	5	use	use	VERB
bracis-33554	28	6	the	the	DET
bracis-33554	28	7	average	average	ADJ
bracis-33554	28	8	reward	reward	NOUN
bracis-33554	28	9	criterion	criterion	NOUN
bracis-33554	28	10	and	and	CCONJ
bracis-33554	28	11	consider	consider	VERB
bracis-33554	28	12	risk	risk	NOUN
bracis-33554	28	13	during	during	ADP
bracis-33554	28	14	the	the	DET
bracis-33554	28	15	process	process	NOUN
bracis-33554	28	16	are	be	AUX
bracis-33554	28	17	those	those	PRON
bracis-33554	28	18	that	that	PRON
bracis-33554	28	19	use	use	VERB
bracis-33554	28	20	exponential	exponential	ADJ
bracis-33554	28	21	utility	utility	NOUN
bracis-33554	28	22	functions	function	NOUN
bracis-33554	28	23	[	[	X
bracis-33554	28	24	2	2	NUM
bracis-33554	28	25	]	]	PUNCT
bracis-33554	28	26	and	and	CCONJ
bracis-33554	28	27	cvar	cvar	NOUN
bracis-33554	28	28	[	[	X
bracis-33554	28	29	7	7	NUM
bracis-33554	28	30	]	]	PUNCT
bracis-33554	28	31	(	(	PUNCT
bracis-33554	28	32	referred	refer	VERB
bracis-33554	28	33	to	to	ADP
bracis-33554	28	34	as	as	ADV
bracis-33554	28	35	steady	steady	ADJ
bracis-33554	28	36	cvar	cvar	NOUN
bracis-33554	28	37	or	or	CCONJ
bracis-33554	28	38	long	long	ADV
bracis-33554	28	39	-	-	PUNCT
bracis-33554	28	40	run	run	NOUN
bracis-33554	28	41	cvar	cvar	NOUN
bracis-33554	28	42	)	)	PUNCT
bracis-33554	28	43	.	.	PUNCT
bracis-33554	29	1	while	while	SCONJ
bracis-33554	29	2	the	the	DET
bracis-33554	29	3	algorithm	algorithm	NOUN
bracis-33554	29	4	that	that	PRON
bracis-33554	29	5	considers	consider	VERB
bracis-33554	29	6	an	an	DET
bracis-33554	29	7	exponential	exponential	ADJ
bracis-33554	29	8	utility	utility	NOUN
bracis-33554	29	9	function	function	NOUN
bracis-33554	29	10	[	[	X
bracis-33554	29	11	2	2	X
bracis-33554	29	12	]	]	PUNCT
bracis-33554	29	13	calculates	calculate	VERB
bracis-33554	29	14	the	the	DET
bracis-33554	29	15	accumulated	accumulate	VERB
bracis-33554	29	16	reward	reward	NOUN
bracis-33554	29	17	and	and	CCONJ
bracis-33554	29	18	how	how	SCONJ
bracis-33554	29	19	much	much	ADJ
bracis-33554	29	20	is	be	AUX
bracis-33554	29	21	added	add	VERB
bracis-33554	29	22	to	to	ADP
bracis-33554	29	23	this	this	DET
bracis-33554	29	24	sum	sum	NOUN
bracis-33554	29	25	,	,	PUNCT
bracis-33554	29	26	thus	thus	ADV
bracis-33554	29	27	following	follow	VERB
bracis-33554	29	28	the	the	DET
bracis-33554	29	29	\(h=\infty	\(h=\infty	ADJ
bracis-33554	29	30	\	\	NOUN
bracis-33554	29	31	)	)	PUNCT
bracis-33554	29	32	approach	approach	NOUN
bracis-33554	29	33	;	;	PUNCT
bracis-33554	29	34	the	the	DET
bracis-33554	29	35	long	long	ADV
bracis-33554	29	36	-	-	PUNCT
bracis-33554	29	37	run	run	VERB
bracis-33554	29	38	cvar	cvar	NOUN
bracis-33554	29	39	algorithm	algorithm	NOUN
bracis-33554	29	40	[	[	X
bracis-33554	29	41	7	7	X
bracis-33554	29	42	]	]	PUNCT
bracis-33554	29	43	calculates	calculate	VERB
bracis-33554	29	44	the	the	DET
bracis-33554	29	45	steady	steady	ADJ
bracis-33554	29	46	-	-	PUNCT
bracis-33554	29	47	state	state	NOUN
bracis-33554	29	48	distribution	distribution	NOUN
bracis-33554	29	49	and	and	CCONJ
bracis-33554	29	50	considers	consider	VERB
bracis-33554	29	51	the	the	DET
bracis-33554	29	52	immediate	immediate	ADJ
bracis-33554	29	53	reward	reward	NOUN
bracis-33554	29	54	,	,	PUNCT
bracis-33554	29	55	which	which	PRON
bracis-33554	29	56	corresponds	correspond	VERB
bracis-33554	29	57	to	to	ADP
bracis-33554	29	58	the	the	DET
bracis-33554	29	59	\(h=1\	\(h=1\	NOUN
bracis-33554	29	60	)	)	PUNCT
bracis-33554	29	61	approach	approach	NOUN
bracis-33554	29	62	.	.	PUNCT
bracis-33554	30	1	the	the	DET
bracis-33554	30	2	objective	objective	NOUN
bracis-33554	30	3	of	of	ADP
bracis-33554	30	4	this	this	DET
bracis-33554	30	5	work	work	NOUN
bracis-33554	30	6	is	be	AUX
bracis-33554	30	7	to	to	PART
bracis-33554	30	8	propose	propose	VERB
bracis-33554	30	9	a	a	DET
bracis-33554	30	10	mathematical	mathematical	ADJ
bracis-33554	30	11	framework	framework	NOUN
bracis-33554	30	12	that	that	PRON
bracis-33554	30	13	provides	provide	VERB
bracis-33554	30	14	a	a	DET
bracis-33554	30	15	unified	unified	ADJ
bracis-33554	30	16	treatment	treatment	NOUN
bracis-33554	30	17	of	of	ADP
bracis-33554	30	18	the	the	DET
bracis-33554	30	19	literature	literature	NOUN
bracis-33554	30	20	on	on	ADP
bracis-33554	30	21	average	average	ADJ
bracis-33554	30	22	reward	reward	NOUN
bracis-33554	30	23	and	and	CCONJ
bracis-33554	30	24	risk	risk	NOUN
bracis-33554	30	25	in	in	ADP
bracis-33554	30	26	mdps	mdps	NOUN
bracis-33554	30	27	,	,	PUNCT
bracis-33554	30	28	including	include	VERB
bracis-33554	30	29	works	work	NOUN
bracis-33554	30	30	that	that	PRON
bracis-33554	30	31	use	use	VERB
bracis-33554	30	32	exponential	exponential	ADJ
bracis-33554	30	33	utility	utility	NOUN
bracis-33554	30	34	functions	function	NOUN
bracis-33554	30	35	[	[	X
bracis-33554	30	36	2	2	NUM
bracis-33554	30	37	]	]	PUNCT
bracis-33554	30	38	and	and	CCONJ
bracis-33554	30	39	cvar	cvar	NOUN
bracis-33554	30	40	[	[	X
bracis-33554	30	41	7	7	NUM
bracis-33554	30	42	]	]	PUNCT
bracis-33554	30	43	,	,	PUNCT
bracis-33554	30	44	as	as	ADV
bracis-33554	30	45	well	well	ADV
bracis-33554	30	46	as	as	ADP
bracis-33554	30	47	to	to	PART
bracis-33554	30	48	include	include	VERB
bracis-33554	30	49	interpretations	interpretation	NOUN
bracis-33554	30	50	with	with	ADP
bracis-33554	30	51	\(1	\(1	PROPN
bracis-33554	30	52	\le	\le	PROPN
bracis-33554	30	53	h	h	NOUN
bracis-33554	30	54	\le	\le	PROPN
bracis-33554	30	55	\infty	\infty	PROPN
bracis-33554	30	56	\	\	PROPN
bracis-33554	30	57	)	)	PUNCT
bracis-33554	30	58	,	,	PUNCT
bracis-33554	30	59	allowing	allow	VERB
bracis-33554	30	60	differentiation	differentiation	NOUN
bracis-33554	30	61	of	of	ADP
bracis-33554	30	62	policies	policy	NOUN
bracis-33554	30	63	that	that	PRON
bracis-33554	30	64	may	may	AUX
bracis-33554	30	65	not	not	PART
bracis-33554	30	66	be	be	AUX
bracis-33554	30	67	distinguished	distinguish	VERB
bracis-33554	30	68	with	with	ADP
bracis-33554	30	69	existing	exist	VERB
bracis-33554	30	70	criteria	criterion	NOUN
bracis-33554	30	71	.	.	PUNCT
bracis-33554	31	1	this	this	DET
bracis-33554	31	2	paper	paper	NOUN
bracis-33554	31	3	is	be	AUX
bracis-33554	31	4	organized	organize	VERB
bracis-33554	31	5	as	as	SCONJ
bracis-33554	31	6	follows	follow	VERB
bracis-33554	31	7	.	.	PUNCT
bracis-33554	32	1	section	section	NOUN
bracis-33554	32	2	 	 	SPACE
bracis-33554	32	3	2	2	NUM
bracis-33554	32	4	reviews	review	VERB
bracis-33554	32	5	the	the	DET
bracis-33554	32	6	definitions	definition	NOUN
bracis-33554	32	7	of	of	ADP
bracis-33554	32	8	mdp	mdp	PROPN
bracis-33554	32	9	,	,	PUNCT
bracis-33554	32	10	average	average	ADJ
bracis-33554	32	11	reward	reward	NOUN
bracis-33554	32	12	criterion	criterion	NOUN
bracis-33554	32	13	,	,	PUNCT
bracis-33554	32	14	and	and	CCONJ
bracis-33554	32	15	risk	risk	NOUN
bracis-33554	32	16	-	-	PUNCT
bracis-33554	32	17	sensitive	sensitive	ADJ
bracis-33554	32	18	average	average	ADJ
bracis-33554	32	19	reward	reward	NOUN
bracis-33554	32	20	literature	literature	NOUN
bracis-33554	32	21	.	.	PUNCT
bracis-33554	33	1	section	section	NOUN
bracis-33554	33	2	 	 	SPACE
bracis-33554	33	3	3	3	NUM
bracis-33554	33	4	presents	present	VERB
bracis-33554	33	5	the	the	DET
bracis-33554	33	6	proposed	propose	VERB
bracis-33554	33	7	framework	framework	NOUN
bracis-33554	33	8	.	.	PUNCT
bracis-33554	34	1	section	section	NOUN
bracis-33554	34	2	 	 	SPACE
bracis-33554	34	3	4	4	NUM
bracis-33554	34	4	evaluates	evaluate	VERB
bracis-33554	34	5	the	the	DET
bracis-33554	34	6	policies	policy	NOUN
bracis-33554	34	7	of	of	ADP
bracis-33554	34	8	an	an	DET
bracis-33554	34	9	mdp	mdp	NOUN
bracis-33554	34	10	for	for	ADP
bracis-33554	34	11	risk	risk	NOUN
bracis-33554	34	12	-	-	PUNCT
bracis-33554	34	13	neutral	neutral	ADJ
bracis-33554	34	14	and	and	CCONJ
bracis-33554	34	15	risk	risk	NOUN
bracis-33554	34	16	-	-	PUNCT
bracis-33554	34	17	sensitive	sensitive	ADJ
bracis-33554	34	18	criteria	criterion	NOUN
bracis-33554	34	19	with	with	ADP
bracis-33554	34	20	the	the	DET
bracis-33554	34	21	proposed	propose	VERB
bracis-33554	34	22	framework	framework	NOUN
bracis-33554	34	23	.	.	PUNCT
bracis-33554	35	1	finally	finally	ADV
bracis-33554	35	2	,	,	PUNCT
bracis-33554	35	3	sect	sect	NOUN
bracis-33554	35	4	.	.	PUNCT
bracis-33554	35	5	 	 	SPACE
bracis-33554	35	6	5	5	NUM
bracis-33554	35	7	presents	present	VERB
bracis-33554	35	8	the	the	DET
bracis-33554	35	9	conclusions	conclusion	NOUN
bracis-33554	35	10	.	.	PUNCT
bracis-33554	36	1	2	2	NUM
bracis-33554	36	2	background	background	NOUN
bracis-33554	36	3	a	a	DET
bracis-33554	36	4	markov	markov	NOUN
bracis-33554	36	5	decision	decision	NOUN
bracis-33554	36	6	process	process	NOUN
bracis-33554	36	7	[	[	X
bracis-33554	36	8	4	4	X
bracis-33554	36	9	]	]	PUNCT
bracis-33554	36	10	is	be	AUX
bracis-33554	36	11	described	describe	VERB
bracis-33554	36	12	by	by	ADP
bracis-33554	36	13	a	a	DET
bracis-33554	36	14	tuple	tuple	NOUN
bracis-33554	36	15	\(\mathcal	\(\mathcal	PUNCT
bracis-33554	36	16	{	{	PUNCT
bracis-33554	36	17	m}=\langle	m}=\langle	PROPN
bracis-33554	36	18	s	s	PROPN
bracis-33554	36	19	,	,	PUNCT
bracis-33554	36	20	a	a	PRON
bracis-33554	36	21	,	,	PUNCT
bracis-33554	36	22	p	p	X
bracis-33554	36	23	,	,	PUNCT
bracis-33554	36	24	r\rangle	r\rangle	VERB
bracis-33554	36	25	\	\	NOUN
bracis-33554	36	26	)	)	PUNCT
bracis-33554	36	27	where	where	SCONJ
bracis-33554	36	28	:	:	PUNCT
bracis-33554	36	29	s	s	X
bracis-33554	36	30	is	be	AUX
bracis-33554	36	31	a	a	DET
bracis-33554	36	32	finite	finite	ADJ
bracis-33554	36	33	set	set	NOUN
bracis-33554	36	34	of	of	ADP
bracis-33554	36	35	states	state	NOUN
bracis-33554	36	36	;	;	PUNCT
bracis-33554	36	37	a	a	PRON
bracis-33554	36	38	is	be	AUX
bracis-33554	36	39	a	a	DET
bracis-33554	36	40	finite	finite	ADJ
bracis-33554	36	41	set	set	NOUN
bracis-33554	36	42	of	of	ADP
bracis-33554	36	43	actions	action	NOUN
bracis-33554	36	44	;	;	PUNCT
bracis-33554	36	45	\(p	\(p	NOUN
bracis-33554	36	46	:	:	PUNCT
bracis-33554	36	47	s	s	AUX
bracis-33554	36	48	\times	\time	VERB
bracis-33554	36	49	a	a	DET
bracis-33554	36	50	\times	\time	NOUN
bracis-33554	36	51	s	s	VERB
bracis-33554	36	52	\rightarrow	\rightarrow	PROPN
bracis-33554	36	53	[	[	X
bracis-33554	36	54	0,1]\	0,1]\	NOUN
bracis-33554	36	55	)	)	PUNCT
bracis-33554	36	56	is	be	AUX
bracis-33554	36	57	a	a	DET
bracis-33554	36	58	transition	transition	NOUN
bracis-33554	36	59	function	function	NOUN
bracis-33554	36	60	that	that	PRON
bracis-33554	36	61	represents	represent	VERB
bracis-33554	36	62	the	the	DET
bracis-33554	36	63	probability	probability	NOUN
bracis-33554	36	64	that	that	PRON
bracis-33554	36	65	\(j	\(j	VERB
bracis-33554	36	66	\in	\in	PROPN
bracis-33554	36	67	s\	s\	NOUN
bracis-33554	36	68	)	)	PUNCT
bracis-33554	36	69	is	be	AUX
bracis-33554	36	70	reached	reach	VERB
bracis-33554	36	71	after	after	SCONJ
bracis-33554	36	72	the	the	DET
bracis-33554	36	73	agent	agent	NOUN
bracis-33554	36	74	executes	execute	VERB
bracis-33554	36	75	an	an	DET
bracis-33554	36	76	action	action	NOUN
bracis-33554	36	77	\(a	\(a	PROPN
bracis-33554	36	78	\in	\in	PROPN
bracis-33554	36	79	a\	a\	PROPN
bracis-33554	36	80	)	)	PUNCT
bracis-33554	36	81	in	in	ADP
bracis-33554	36	82	a	a	DET
bracis-33554	36	83	state	state	NOUN
bracis-33554	36	84	\(s\in	\(s\in	X
bracis-33554	36	85	s\	s\	NOUN
bracis-33554	36	86	)	)	PUNCT
bracis-33554	36	87	,	,	PUNCT
bracis-33554	36	88	i.e.	i.e.	X
bracis-33554	36	89	,	,	PUNCT
bracis-33554	36	90	\(\pr	\(\pr	NOUN
bracis-33554	36	91	(	(	PUNCT
bracis-33554	36	92	s_{n+1}=j	s_{n+1}=j	NOUN
bracis-33554	36	93	|s_{n}=s	|s_{n}=s	NOUN
bracis-33554	36	94	,	,	PUNCT
bracis-33554	36	95	a_{n}=a	a_{n}=a	PUNCT
bracis-33554	36	96	)	)	PUNCT
bracis-33554	37	1	=	=	SYM
bracis-33554	37	2	p(s	p(s	PROPN
bracis-33554	37	3	,	,	PUNCT
bracis-33554	37	4	a	a	PRON
bracis-33554	37	5	,	,	PUNCT
bracis-33554	37	6	j)\	j)\	NUM
bracis-33554	37	7	)	)	PUNCT
bracis-33554	37	8	;	;	PUNCT
bracis-33554	37	9	and	and	CCONJ
bracis-33554	37	10	\(r	\(r	NUM
bracis-33554	37	11	:	:	PUNCT
bracis-33554	37	12	s	s	VERB
bracis-33554	37	13	\times	\time	VERB
bracis-33554	37	14	a	a	DET
bracis-33554	37	15	\rightarrow	\rightarrow	PROPN
bracis-33554	37	16	\mathbb	\mathbb	PROPN
bracis-33554	37	17	{	{	PUNCT
bracis-33554	37	18	r}\	r}\	NUM
bracis-33554	37	19	)	)	PUNCT
bracis-33554	37	20	is	be	AUX
bracis-33554	37	21	a	a	DET
bracis-33554	37	22	reward	reward	NOUN
bracis-33554	37	23	function	function	NOUN
bracis-33554	37	24	that	that	PRON
bracis-33554	37	25	represents	represent	VERB
bracis-33554	37	26	the	the	DET
bracis-33554	37	27	reward	reward	NOUN
bracis-33554	37	28	of	of	ADP
bracis-33554	37	29	executing	execute	VERB
bracis-33554	37	30	an	an	DET
bracis-33554	37	31	action	action	NOUN
bracis-33554	37	32	\(a	\(a	NOUN
bracis-33554	37	33	\in	\in	PROPN
bracis-33554	37	34	a\	a\	PROPN
bracis-33554	37	35	)	)	PUNCT
bracis-33554	37	36	in	in	ADP
bracis-33554	37	37	a	a	DET
bracis-33554	37	38	state	state	NOUN
bracis-33554	37	39	\(s	\(s	ADJ
bracis-33554	37	40	\in	\in	PROPN
bracis-33554	37	41	s\	s\	NOUN
bracis-33554	37	42	)	)	PUNCT
bracis-33554	37	43	.	.	PUNCT
bracis-33554	38	1	in	in	ADP
bracis-33554	38	2	this	this	DET
bracis-33554	38	3	work	work	NOUN
bracis-33554	38	4	,	,	PUNCT
bracis-33554	38	5	the	the	DET
bracis-33554	38	6	average	average	ADJ
bracis-33554	38	7	reward	reward	NOUN
bracis-33554	38	8	criterion	criterion	NOUN
bracis-33554	38	9	is	be	AUX
bracis-33554	38	10	used	use	VERB
bracis-33554	38	11	for	for	ADP
bracis-33554	38	12	infinite	infinite	NOUN
bracis-33554	38	13	-	-	PUNCT
bracis-33554	38	14	horizon	horizon	NOUN
bracis-33554	38	15	problems	problem	NOUN
bracis-33554	38	16	.	.	PUNCT
bracis-33554	39	1	the	the	DET
bracis-33554	39	2	average	average	ADJ
bracis-33554	39	3	reward	reward	NOUN
bracis-33554	39	4	criterion	criterion	NOUN
bracis-33554	39	5	depends	depend	VERB
bracis-33554	39	6	on	on	ADP
bracis-33554	39	7	the	the	DET
bracis-33554	39	8	behavior	behavior	NOUN
bracis-33554	39	9	of	of	ADP
bracis-33554	39	10	the	the	DET
bracis-33554	39	11	stochastic	stochastic	ADJ
bracis-33554	39	12	process	process	NOUN
bracis-33554	39	13	in	in	ADP
bracis-33554	39	14	the	the	DET
bracis-33554	39	15	limit	limit	NOUN
bracis-33554	39	16	,	,	PUNCT
bracis-33554	39	17	which	which	PRON
bracis-33554	39	18	determines	determine	VERB
bracis-33554	39	19	certain	certain	ADJ
bracis-33554	39	20	models	model	NOUN
bracis-33554	39	21	of	of	ADP
bracis-33554	39	22	the	the	DET
bracis-33554	39	23	criterion	criterion	NOUN
bracis-33554	39	24	based	base	VERB
bracis-33554	39	25	on	on	ADP
bracis-33554	39	26	the	the	DET
bracis-33554	39	27	structure	structure	NOUN
bracis-33554	39	28	of	of	ADP
bracis-33554	39	29	the	the	DET
bracis-33554	39	30	markov	markov	NOUN
bracis-33554	39	31	chain	chain	NOUN
bracis-33554	39	32	generated	generate	VERB
bracis-33554	39	33	from	from	ADP
bracis-33554	39	34	stationary	stationary	ADJ
bracis-33554	39	35	policies	policy	NOUN
bracis-33554	39	36	.	.	PUNCT
bracis-33554	40	1	among	among	ADP
bracis-33554	40	2	the	the	DET
bracis-33554	40	3	types	type	NOUN
bracis-33554	40	4	of	of	ADP
bracis-33554	40	5	markov	markov	NOUN
bracis-33554	40	6	chains	chain	NOUN
bracis-33554	40	7	are	be	AUX
bracis-33554	40	8	unichain	unichain	ADJ
bracis-33554	40	9	,	,	PUNCT
bracis-33554	40	10	multichain	multichain	NOUN
bracis-33554	40	11	,	,	PUNCT
bracis-33554	40	12	recurrent	recurrent	NOUN
bracis-33554	40	13	,	,	PUNCT
bracis-33554	40	14	ergodic	ergodic	ADJ
bracis-33554	40	15	,	,	PUNCT
bracis-33554	40	16	and	and	CCONJ
bracis-33554	40	17	aperiodic	aperiodic	ADJ
bracis-33554	40	18	chains	chain	NOUN
bracis-33554	40	19	.	.	PUNCT
bracis-33554	41	1	a	a	DET
bracis-33554	41	2	unichain	unichain	ADJ
bracis-33554	41	3	markov	markov	NOUN
bracis-33554	41	4	chain	chain	NOUN
bracis-33554	41	5	has	have	VERB
bracis-33554	41	6	a	a	DET
bracis-33554	41	7	closed	closed	ADJ
bracis-33554	41	8	irreducible	irreducible	ADJ
bracis-33554	41	9	set	set	NOUN
bracis-33554	41	10	of	of	ADP
bracis-33554	41	11	states	state	NOUN
bracis-33554	41	12	(	(	PUNCT
bracis-33554	41	13	a	a	DET
bracis-33554	41	14	set	set	NOUN
bracis-33554	41	15	of	of	ADP
bracis-33554	41	16	states	state	NOUN
bracis-33554	41	17	where	where	SCONJ
bracis-33554	41	18	all	all	DET
bracis-33554	41	19	states	state	NOUN
bracis-33554	41	20	communicate	communicate	VERB
bracis-33554	41	21	with	with	ADP
bracis-33554	41	22	each	each	DET
bracis-33554	41	23	other	other	ADJ
bracis-33554	41	24	and	and	CCONJ
bracis-33554	41	25	do	do	AUX
bracis-33554	41	26	not	not	PART
bracis-33554	41	27	communicate	communicate	VERB
bracis-33554	41	28	with	with	ADP
bracis-33554	41	29	states	state	NOUN
bracis-33554	41	30	outside	outside	ADP
bracis-33554	41	31	the	the	DET
bracis-33554	41	32	set	set	NOUN
bracis-33554	41	33	)	)	PUNCT
bracis-33554	41	34	and	and	CCONJ
bracis-33554	41	35	a	a	DET
bracis-33554	41	36	possibly	possibly	ADV
bracis-33554	41	37	empty	empty	ADJ
bracis-33554	41	38	set	set	NOUN
bracis-33554	41	39	of	of	ADP
bracis-33554	41	40	transient	transient	ADJ
bracis-33554	41	41	states	state	NOUN
bracis-33554	41	42	(	(	PUNCT
bracis-33554	41	43	states	state	NOUN
bracis-33554	41	44	that	that	PRON
bracis-33554	41	45	will	will	AUX
bracis-33554	41	46	not	not	PART
bracis-33554	41	47	be	be	AUX
bracis-33554	41	48	revisited	revisit	VERB
bracis-33554	41	49	after	after	ADP
bracis-33554	41	50	some	some	DET
bracis-33554	41	51	point	point	NOUN
bracis-33554	41	52	in	in	ADP
bracis-33554	41	53	time	time	NOUN
bracis-33554	41	54	)	)	PUNCT
bracis-33554	41	55	.	.	PUNCT
bracis-33554	42	1	otherwise	otherwise	ADV
bracis-33554	42	2	,	,	PUNCT
bracis-33554	42	3	the	the	DET
bracis-33554	42	4	markov	markov	NOUN
bracis-33554	42	5	chain	chain	NOUN
bracis-33554	42	6	is	be	AUX
bracis-33554	42	7	multichain	multichain	ADJ
bracis-33554	42	8	.	.	PUNCT
bracis-33554	43	1	a	a	DET
bracis-33554	43	2	recurrent	recurrent	ADJ
bracis-33554	43	3	markov	markov	NOUN
bracis-33554	43	4	chain	chain	NOUN
bracis-33554	43	5	is	be	AUX
bracis-33554	43	6	a	a	DET
bracis-33554	43	7	unichain	unichain	NOUN
bracis-33554	43	8	chain	chain	NOUN
bracis-33554	43	9	where	where	SCONJ
bracis-33554	43	10	the	the	DET
bracis-33554	43	11	set	set	NOUN
bracis-33554	43	12	of	of	ADP
bracis-33554	43	13	transient	transient	ADJ
bracis-33554	43	14	states	state	NOUN
bracis-33554	43	15	is	be	AUX
bracis-33554	43	16	empty	empty	ADJ
bracis-33554	43	17	.	.	PUNCT
bracis-33554	44	1	a	a	DET
bracis-33554	44	2	markov	markov	NOUN
bracis-33554	44	3	chain	chain	NOUN
bracis-33554	44	4	is	be	AUX
bracis-33554	44	5	ergodic	ergodic	ADJ
bracis-33554	44	6	if	if	SCONJ
bracis-33554	44	7	it	it	PRON
bracis-33554	44	8	is	be	AUX
bracis-33554	44	9	recurrent	recurrent	ADJ
bracis-33554	44	10	and	and	CCONJ
bracis-33554	44	11	aperiodic	aperiodic	ADJ
bracis-33554	44	12	.	.	PUNCT
bracis-33554	45	1	a	a	DET
bracis-33554	45	2	markov	markov	NOUN
bracis-33554	45	3	chain	chain	NOUN
bracis-33554	45	4	is	be	AUX
bracis-33554	45	5	aperiodic	aperiodic	ADJ
bracis-33554	45	6	if	if	SCONJ
bracis-33554	45	7	the	the	DET
bracis-33554	45	8	returns	return	NOUN
bracis-33554	45	9	to	to	ADP
bracis-33554	45	10	states	state	NOUN
bracis-33554	45	11	occur	occur	VERB
bracis-33554	45	12	at	at	ADP
bracis-33554	45	13	irregular	irregular	ADJ
bracis-33554	45	14	intervals	interval	NOUN
bracis-33554	45	15	.	.	PUNCT
bracis-33554	46	1	2.1	2.1	NUM
bracis-33554	46	2	risk	risk	NOUN
bracis-33554	46	3	-	-	PUNCT
bracis-33554	46	4	neutral	neutral	ADJ
bracis-33554	46	5	criterion	criterion	NOUN
bracis-33554	46	6	the	the	DET
bracis-33554	46	7	expected	expected	ADJ
bracis-33554	46	8	total	total	ADJ
bracis-33554	46	9	reward	reward	NOUN
bracis-33554	46	10	of	of	ADP
bracis-33554	46	11	a	a	DET
bracis-33554	46	12	policy	policy	NOUN
bracis-33554	46	13	\(\pi	\(\pi	ADP
bracis-33554	46	14	\	\	NOUN
bracis-33554	46	15	)	)	PUNCT
bracis-33554	46	16	from	from	ADP
bracis-33554	46	17	the	the	DET
bracis-33554	46	18	initial	initial	ADJ
bracis-33554	46	19	state	state	NOUN
bracis-33554	46	20	s	s	VERB
bracis-33554	46	21	up	up	ADV
bracis-33554	46	22	 	 	SPACE
bracis-33554	46	23	to	to	ADP
bracis-33554	46	24	the	the	DET
bracis-33554	46	25	decision	decision	NOUN
bracis-33554	46	26	epoch	epoch	NOUN
bracis-33554	46	27	\(n+1\	\(n+1\	NOUN
bracis-33554	46	28	)	)	PUNCT
bracis-33554	46	29	is	be	AUX
bracis-33554	46	30	a	a	DET
bracis-33554	46	31	function	function	NOUN
bracis-33554	46	32	\(v^\pi	\(v^\pi	PUNCT
bracis-33554	47	1	_	_	PUNCT
bracis-33554	47	2	{	{	PUNCT
bracis-33554	47	3	n+1}\	n+1}\	ADV
bracis-33554	47	4	)	)	PUNCT
bracis-33554	47	5	defined	define	VERB
bracis-33554	47	6	 	 	SPACE
bracis-33554	47	7	by	by	ADP
bracis-33554	47	8	$	$	SYM
bracis-33554	47	9	$	$	SYM
bracis-33554	47	10	\begin{aligned	\begin{aligne	VERB
bracis-33554	47	11	}	}	PUNCT
bracis-33554	47	12	v^\pi	v^\pi	NOUN
bracis-33554	47	13	_	_	PRON
bracis-33554	47	14	{	{	PUNCT
bracis-33554	47	15	n+1}(s	n+1}(s	X
bracis-33554	47	16	)	)	PUNCT
bracis-33554	48	1	=	=	SYM
bracis-33554	48	2	e	e	X
bracis-33554	48	3	\bigg	\bigg	ADP
bracis-33554	48	4	\	\	PROPN
bracis-33554	48	5	{	{	PUNCT
bracis-33554	48	6	\sum	\sum	NOUN
bracis-33554	48	7	_	_	PUNCT
bracis-33554	48	8	{	{	PUNCT
bracis-33554	48	9	n=1}^{n	n=1}^{n	ADJ
bracis-33554	48	10	}	}	PUNCT
bracis-33554	48	11	r(s_n	r(s_n	NOUN
bracis-33554	48	12	,	,	PUNCT
bracis-33554	48	13	a_n	a_n	NUM
bracis-33554	48	14	)	)	PUNCT
bracis-33554	48	15	\big	\big	NOUN
bracis-33554	48	16	|	|	CCONJ
bracis-33554	48	17	s_1	s_1	PROPN
bracis-33554	48	18	=	=	SYM
bracis-33554	48	19	s,\pi	s,\pi	PROPN
bracis-33554	48	20	\bigg	\bigg	ADP
bracis-33554	48	21	\	\	NOUN
bracis-33554	48	22	}	}	PUNCT
bracis-33554	48	23	=	=	SYM
bracis-33554	48	24	e	e	X
bracis-33554	48	25	\bigg	\bigg	ADP
bracis-33554	48	26	\	\	PROPN
bracis-33554	48	27	{	{	PUNCT
bracis-33554	48	28	\sum	\sum	NOUN
bracis-33554	48	29	_	_	PUNCT
bracis-33554	48	30	{	{	PUNCT
bracis-33554	48	31	n=1}^{n	n=1}^{n	ADV
bracis-33554	48	32	}	}	PUNCT
bracis-33554	48	33	r_n	r_n	PROPN
bracis-33554	48	34	\bigg	\bigg	ADP
bracis-33554	48	35	\	\	NOUN
bracis-33554	48	36	}	}	PUNCT
bracis-33554	48	37	,	,	PUNCT
bracis-33554	48	38	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	48	39	(	(	PUNCT
bracis-33554	48	40	1	1	NUM
bracis-33554	48	41	)	)	PUNCT
bracis-33554	48	42	where	where	SCONJ
bracis-33554	48	43	\(s_n\	\(s_n\	PROPN
bracis-33554	48	44	)	)	PUNCT
bracis-33554	48	45	and	and	CCONJ
bracis-33554	48	46	\(a_n\	\(a_n\	NOUN
bracis-33554	48	47	)	)	PUNCT
bracis-33554	48	48	refer	refer	VERB
bracis-33554	48	49	to	to	ADP
bracis-33554	48	50	the	the	DET
bracis-33554	48	51	random	random	ADJ
bracis-33554	48	52	variables	variable	NOUN
bracis-33554	48	53	of	of	ADP
bracis-33554	48	54	the	the	DET
bracis-33554	48	55	state	state	NOUN
bracis-33554	48	56	and	and	CCONJ
bracis-33554	48	57	action	action	NOUN
bracis-33554	48	58	in	in	ADP
bracis-33554	48	59	the	the	DET
bracis-33554	48	60	time	time	NOUN
bracis-33554	48	61	step	step	NOUN
bracis-33554	48	62	n.	n.	NOUN
bracis-33554	48	63	when	when	SCONJ
bracis-33554	48	64	n	n	PRON
bracis-33554	48	65	tends	tend	VERB
bracis-33554	48	66	to	to	PART
bracis-33554	48	67	infinity	infinity	VERB
bracis-33554	48	68	,	,	PUNCT
bracis-33554	48	69	\(v^\pi	\(v^\pi	X
bracis-33554	48	70	_	_	PUNCT
bracis-33554	48	71	{	{	PUNCT
bracis-33554	48	72	n+1}(s)\	n+1}(s)\	CCONJ
bracis-33554	48	73	)	)	PUNCT
bracis-33554	48	74	diverges	diverge	NOUN
bracis-33554	48	75	.	.	PUNCT
bracis-33554	49	1	the	the	DET
bracis-33554	49	2	expected	expect	VERB
bracis-33554	49	3	average	average	ADJ
bracis-33554	49	4	reward	reward	NOUN
bracis-33554	49	5	of	of	ADP
bracis-33554	49	6	a	a	DET
bracis-33554	49	7	policy	policy	NOUN
bracis-33554	49	8	\(\pi	\(\pi	ADP
bracis-33554	49	9	\	\	NOUN
bracis-33554	49	10	)	)	PUNCT
bracis-33554	49	11	,	,	PUNCT
bracis-33554	49	12	i.e.	i.e.	X
bracis-33554	49	13	the	the	DET
bracis-33554	49	14	gain	gain	NOUN
bracis-33554	49	15	of	of	ADP
bracis-33554	49	16	a	a	DET
bracis-33554	49	17	policy	policy	NOUN
bracis-33554	49	18	\(\pi	\(\pi	ADP
bracis-33554	49	19	\	\	NOUN
bracis-33554	49	20	)	)	PUNCT
bracis-33554	49	21	,	,	PUNCT
bracis-33554	49	22	 	 	SPACE
bracis-33554	49	23	is	be	AUX
bracis-33554	49	24	$	$	SYM
bracis-33554	49	25	$	$	SYM
bracis-33554	49	26	\begin{aligned	\begin{aligne	VERB
bracis-33554	49	27	}	}	PUNCT
bracis-33554	49	28	\begin{aligned	\begin{aligne	VERB
bracis-33554	49	29	}	}	PUNCT
bracis-33554	49	30	g^\pi	g^\pi	PROPN
bracis-33554	49	31	(	(	PUNCT
bracis-33554	49	32	s	s	NOUN
bracis-33554	49	33	)	)	PUNCT
bracis-33554	49	34	&	&	CCONJ
bracis-33554	49	35	=	=	SYM
bracis-33554	49	36	\lim	\lim	PROPN
bracis-33554	49	37	_	_	PUNCT
bracis-33554	49	38	{	{	PUNCT
bracis-33554	49	39	n\rightarrow	n\rightarrow	NOUN
bracis-33554	49	40	\infty	\infty	PROPN
bracis-33554	49	41	}	}	PUNCT
bracis-33554	49	42	\frac{1}{n	\frac{1}{n	NOUN
bracis-33554	49	43	}	}	PUNCT
bracis-33554	49	44	v^\pi	v^\pi	VERB
bracis-33554	49	45	_	_	PRON
bracis-33554	49	46	{	{	PUNCT
bracis-33554	49	47	n+1}(s	n+1}(s	NOUN
bracis-33554	49	48	)	)	PUNCT
bracis-33554	49	49	\\	\\	NOUN
bracis-33554	49	50	&	&	CCONJ
bracis-33554	49	51	=	=	NOUN
bracis-33554	49	52	\lim	\lim	PROPN
bracis-33554	49	53	_	_	PUNCT
bracis-33554	49	54	{	{	PUNCT
bracis-33554	49	55	n\rightarrow	n\rightarrow	NOUN
bracis-33554	49	56	\infty	\infty	PROPN
bracis-33554	49	57	}	}	PUNCT
bracis-33554	49	58	\frac{1}{n	\frac{1}{n	NOUN
bracis-33554	49	59	}	}	PUNCT
bracis-33554	49	60	\sum	\sum	NOUN
bracis-33554	49	61	_	_	PUNCT
bracis-33554	49	62	{	{	PUNCT
bracis-33554	49	63	n=1}^{n	n=1}^{n	ADV
bracis-33554	49	64	}	}	PUNCT
bracis-33554	49	65	p^{n-1}_{\pi	p^{n-1}_{\pi	NOUN
bracis-33554	49	66	}	}	PUNCT
bracis-33554	49	67	r_{\pi	r_{\pi	NOUN
bracis-33554	49	68	}	}	PUNCT
bracis-33554	49	69	(	(	PUNCT
bracis-33554	49	70	s	s	NOUN
bracis-33554	49	71	)	)	PUNCT
bracis-33554	49	72	,	,	PUNCT
bracis-33554	49	73	\end{aligned	\end{aligne	VERB
bracis-33554	49	74	}	}	PUNCT
bracis-33554	49	75	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	49	76	(	(	PUNCT
bracis-33554	49	77	2	2	NUM
bracis-33554	49	78	)	)	PUNCT
bracis-33554	49	79	where	where	SCONJ
bracis-33554	49	80	\(p^{n}_{\pi	\(p^{n}_{\pi	VERB
bracis-33554	49	81	}	}	PUNCT
bracis-33554	49	82	\	\	NOUN
bracis-33554	49	83	)	)	PUNCT
bracis-33554	49	84	is	be	AUX
bracis-33554	49	85	the	the	DET
bracis-33554	49	86	n	n	ADV
bracis-33554	49	87	-	-	PUNCT
bracis-33554	49	88	th	th	VERB
bracis-33554	49	89	power	power	NOUN
bracis-33554	49	90	of	of	ADP
bracis-33554	49	91	the	the	DET
bracis-33554	49	92	transition	transition	NOUN
bracis-33554	49	93	matrix	matrix	NOUN
bracis-33554	49	94	\(p_\pi	\(p_\pi	X
bracis-33554	49	95	\	\	NOUN
bracis-33554	49	96	)	)	PUNCT
bracis-33554	49	97	and	and	CCONJ
bracis-33554	49	98	\(r_{\pi	\(r_{\pi	NOUN
bracis-33554	49	99	}	}	PUNCT
bracis-33554	49	100	\	\	NOUN
bracis-33554	49	101	)	)	PUNCT
bracis-33554	49	102	is	be	AUX
bracis-33554	49	103	the	the	DET
bracis-33554	49	104	reward	reward	NOUN
bracis-33554	49	105	function	function	NOUN
bracis-33554	49	106	of	of	ADP
bracis-33554	49	107	\(\pi	\(\pi	PROPN
bracis-33554	49	108	\	\	NOUN
bracis-33554	49	109	)	)	PUNCT
bracis-33554	49	110	.	.	PUNCT
bracis-33554	50	1	a	a	DET
bracis-33554	50	2	policy	policy	NOUN
bracis-33554	50	3	with	with	ADP
bracis-33554	50	4	the	the	DET
bracis-33554	50	5	highest	high	ADJ
bracis-33554	50	6	gain	gain	NOUN
bracis-33554	50	7	\(g^*(s)\	\(g^*(s)\	NUM
bracis-33554	50	8	)	)	PUNCT
bracis-33554	50	9	is	be	AUX
bracis-33554	50	10	called	call	VERB
bracis-33554	50	11	the	the	DET
bracis-33554	50	12	optimal	optimal	ADJ
bracis-33554	50	13	policy	policy	NOUN
bracis-33554	50	14	\(\pi	\(\pi	PROPN
bracis-33554	50	15	^*\	^*\	X
bracis-33554	50	16	)	)	PUNCT
bracis-33554	50	17	,	,	PUNCT
bracis-33554	50	18	$	$	SYM
bracis-33554	50	19	$	$	SYM
bracis-33554	50	20	\begin{aligned	\begin{aligne	VERB
bracis-33554	50	21	}	}	PUNCT
bracis-33554	50	22	g^*(s	g^*(s	PROPN
bracis-33554	50	23	)	)	PUNCT
bracis-33554	51	1	=	=	PUNCT
bracis-33554	51	2	g^{\pi	g^{\pi	NOUN
bracis-33554	51	3	^*}(s	^*}(s	ADP
bracis-33554	51	4	)	)	PUNCT
bracis-33554	52	1	=	=	SYM
bracis-33554	52	2	\sup	\sup	NOUN
bracis-33554	52	3	_	_	PUNCT
bracis-33554	52	4	{	{	PUNCT
bracis-33554	52	5	\pi	\pi	PROPN
bracis-33554	52	6	\in	\in	PROPN
bracis-33554	52	7	\varpi	\varpi	PROPN
bracis-33554	52	8	}	}	PUNCT
bracis-33554	52	9	g^\pi	g^\pi	PROPN
bracis-33554	52	10	(	(	PUNCT
bracis-33554	52	11	s	s	NOUN
bracis-33554	52	12	)	)	PUNCT
bracis-33554	52	13	,	,	PUNCT
bracis-33554	52	14	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	52	15	(	(	PUNCT
bracis-33554	52	16	3	3	NUM
bracis-33554	52	17	)	)	PUNCT
bracis-33554	52	18	where	where	SCONJ
bracis-33554	52	19	\(\varpi	\(\varpi	ADJ
bracis-33554	52	20	\	\	NOUN
bracis-33554	52	21	)	)	PUNCT
bracis-33554	52	22	is	be	AUX
bracis-33554	52	23	the	the	DET
bracis-33554	52	24	set	set	NOUN
bracis-33554	52	25	of	of	ADP
bracis-33554	52	26	stationary	stationary	ADJ
bracis-33554	52	27	policies	policy	NOUN
bracis-33554	52	28	.	.	PUNCT
bracis-33554	53	1	in	in	ADP
bracis-33554	53	2	the	the	DET
bracis-33554	53	3	following	follow	VERB
bracis-33554	53	4	sections	section	NOUN
bracis-33554	53	5	,	,	PUNCT
bracis-33554	53	6	the	the	DET
bracis-33554	53	7	simplified	simplified	ADJ
bracis-33554	53	8	version	version	NOUN
bracis-33554	53	9	of	of	ADP
bracis-33554	53	10	the	the	DET
bracis-33554	53	11	notation	notation	NOUN
bracis-33554	53	12	shown	show	VERB
bracis-33554	53	13	on	on	ADP
bracis-33554	53	14	the	the	DET
bracis-33554	53	15	right	right	ADJ
bracis-33554	53	16	side	side	NOUN
bracis-33554	53	17	of	of	ADP
bracis-33554	53	18	eq	eq	PROPN
bracis-33554	53	19	.	.	PUNCT
bracis-33554	53	20	 	 	SPACE
bracis-33554	53	21	1	1	NUM
bracis-33554	53	22	will	will	AUX
bracis-33554	53	23	be	be	AUX
bracis-33554	53	24	used	use	VERB
bracis-33554	53	25	.	.	PUNCT
bracis-33554	54	1	2.2	2.2	NUM
bracis-33554	54	2	risk	risk	NOUN
bracis-33554	54	3	-	-	PUNCT
bracis-33554	54	4	sensitive	sensitive	ADJ
bracis-33554	54	5	criterion	criterion	NOUN
bracis-33554	54	6	with	with	ADP
bracis-33554	54	7	utility	utility	NOUN
bracis-33554	54	8	function	function	NOUN
bracis-33554	54	9	there	there	PRON
bracis-33554	54	10	are	be	VERB
bracis-33554	54	11	several	several	ADJ
bracis-33554	54	12	ways	way	NOUN
bracis-33554	54	13	to	to	PART
bracis-33554	54	14	incorporate	incorporate	VERB
bracis-33554	54	15	risk	risk	NOUN
bracis-33554	54	16	into	into	ADP
bracis-33554	54	17	decision	decision	NOUN
bracis-33554	54	18	making	making	NOUN
bracis-33554	54	19	with	with	ADP
bracis-33554	54	20	mdps	mdps	PROPN
bracis-33554	54	21	.	.	PUNCT
bracis-33554	55	1	one	one	NUM
bracis-33554	55	2	way	way	NOUN
bracis-33554	55	3	is	be	AUX
bracis-33554	55	4	to	to	PART
bracis-33554	55	5	use	use	VERB
bracis-33554	55	6	a	a	DET
bracis-33554	55	7	utility	utility	NOUN
bracis-33554	55	8	function	function	NOUN
bracis-33554	55	9	\(u	\(u	NOUN
bracis-33554	55	10	:	:	PUNCT
bracis-33554	55	11	\mathbb	\mathbb	PROPN
bracis-33554	55	12	{	{	PUNCT
bracis-33554	55	13	r	r	X
bracis-33554	55	14	}	}	PUNCT
bracis-33554	55	15	\rightarrow	\rightarrow	PROPN
bracis-33554	55	16	\mathbb	\mathbb	PROPN
bracis-33554	55	17	{	{	PUNCT
bracis-33554	55	18	r}\	r}\	NUM
bracis-33554	55	19	)	)	PUNCT
bracis-33554	55	20	,	,	PUNCT
bracis-33554	55	21	such	such	ADJ
bracis-33554	55	22	as	as	ADP
bracis-33554	55	23	the	the	DET
bracis-33554	55	24	exponential	exponential	ADJ
bracis-33554	55	25	utility	utility	NOUN
bracis-33554	55	26	function	function	NOUN
bracis-33554	55	27	[	[	X
bracis-33554	55	28	2	2	NUM
bracis-33554	55	29	]	]	PUNCT
bracis-33554	55	30	.	.	PUNCT
bracis-33554	56	1	the	the	DET
bracis-33554	56	2	exponential	exponential	ADJ
bracis-33554	56	3	utility	utility	NOUN
bracis-33554	56	4	function	function	NOUN
bracis-33554	56	5	u	u	NOUN
bracis-33554	56	6	is	be	AUX
bracis-33554	56	7	defined	define	VERB
bracis-33554	56	8	 	 	SPACE
bracis-33554	56	9	by	by	ADP
bracis-33554	56	10	$	$	SYM
bracis-33554	56	11	$	$	SYM
bracis-33554	56	12	\begin{aligned	\begin{aligne	VERB
bracis-33554	56	13	}	}	PUNCT
bracis-33554	56	14	u(x	u(x	NOUN
bracis-33554	56	15	)	)	PUNCT
bracis-33554	56	16	=	=	SYM
bracis-33554	56	17	-(\text	-(\text	PROPN
bracis-33554	56	18	{	{	PUNCT
bracis-33554	56	19	sgn	sgn	NOUN
bracis-33554	56	20	}	}	PUNCT
bracis-33554	56	21	\gamma	\gamma	NUM
bracis-33554	56	22	)	)	PUNCT
bracis-33554	56	23	e^{-\gamma	e^{-\gamma	X
bracis-33554	57	1	x	x	X
bracis-33554	57	2	}	}	PUNCT
bracis-33554	57	3	,	,	PUNCT
bracis-33554	57	4	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	57	5	(	(	PUNCT
bracis-33554	57	6	4	4	NUM
bracis-33554	57	7	)	)	PUNCT
bracis-33554	57	8	with	with	ADP
bracis-33554	57	9	inverse	inverse	NOUN
bracis-33554	57	10	$	$	SYM
bracis-33554	57	11	$	$	SYM
bracis-33554	57	12	\begin{aligned	\begin{aligne	VERB
bracis-33554	57	13	}	}	PUNCT
bracis-33554	57	14	u^{-1}(y	u^{-1}(y	PROPN
bracis-33554	57	15	)	)	PUNCT
bracis-33554	57	16	=	=	SYM
bracis-33554	57	17	\frac{1}{\gamma	\frac{1}{\gamma	PROPN
bracis-33554	57	18	}	}	PUNCT
bracis-33554	57	19	\text	\text	PROPN
bracis-33554	57	20	{	{	PUNCT
bracis-33554	57	21	ln}[-\text	ln}[-\text	PROPN
bracis-33554	57	22	{	{	PUNCT
bracis-33554	57	23	sgn}(\gamma	sgn}(\gamma	PROPN
bracis-33554	57	24	)	)	PUNCT
bracis-33554	57	25	y	y	PROPN
bracis-33554	57	26	]	]	X
bracis-33554	57	27	,	,	PUNCT
bracis-33554	57	28	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	57	29	(	(	PUNCT
bracis-33554	57	30	5	5	NUM
bracis-33554	57	31	)	)	PUNCT
bracis-33554	57	32	where	where	SCONJ
bracis-33554	57	33	\(\gamma	\(\gamma	ADP
bracis-33554	57	34	\	\	NOUN
bracis-33554	57	35	)	)	PUNCT
bracis-33554	57	36	is	be	AUX
bracis-33554	57	37	the	the	DET
bracis-33554	57	38	risk	risk	NOUN
bracis-33554	57	39	factor	factor	NOUN
bracis-33554	57	40	and	and	CCONJ
bracis-33554	57	41	\(\text	\(\text	NOUN
bracis-33554	57	42	{	{	PUNCT
bracis-33554	57	43	sgn	sgn	NOUN
bracis-33554	57	44	}	}	PUNCT
bracis-33554	57	45	(	(	PUNCT
bracis-33554	57	46	\gamma	\gamma	PROPN
bracis-33554	57	47	)	)	PUNCT
bracis-33554	57	48	\	\	NOUN
bracis-33554	57	49	)	)	PUNCT
bracis-33554	57	50	indicates	indicate	VERB
bracis-33554	57	51	the	the	DET
bracis-33554	57	52	sign	sign	NOUN
bracis-33554	57	53	of	of	ADP
bracis-33554	57	54	\(\gamma	\(\gamma	X
bracis-33554	57	55	\	\	PROPN
bracis-33554	57	56	)	)	PUNCT
bracis-33554	57	57	.	.	PUNCT
bracis-33554	58	1	the	the	DET
bracis-33554	58	2	certainty	certainty	ADJ
bracis-33554	58	3	equivalent	equivalent	ADJ
bracis-33554	58	4	\(v_{u}^{\pi	\(v_{u}^{\pi	NOUN
bracis-33554	58	5	}	}	PUNCT
bracis-33554	58	6	\	\	NOUN
bracis-33554	58	7	)	)	PUNCT
bracis-33554	58	8	is	be	AUX
bracis-33554	58	9	the	the	DET
bracis-33554	58	10	value	value	NOUN
bracis-33554	58	11	whose	whose	DET
bracis-33554	58	12	utility	utility	NOUN
bracis-33554	58	13	is	be	AUX
bracis-33554	58	14	equal	equal	ADJ
bracis-33554	58	15	to	to	ADP
bracis-33554	58	16	the	the	DET
bracis-33554	58	17	utility	utility	NOUN
bracis-33554	58	18	of	of	ADP
bracis-33554	58	19	the	the	DET
bracis-33554	58	20	expected	expect	VERB
bracis-33554	58	21	value	value	NOUN
bracis-33554	58	22	of	of	ADP
bracis-33554	58	23	the	the	DET
bracis-33554	58	24	accumulated	accumulate	VERB
bracis-33554	58	25	reward	reward	NOUN
bracis-33554	58	26	\(v^\pi	\(v^\pi	PUNCT
bracis-33554	58	27	\	\	PROPN
bracis-33554	58	28	)	)	PUNCT
bracis-33554	58	29	,	,	PUNCT
bracis-33554	58	30	i.e.	i.e.	X
bracis-33554	58	31	,	,	PUNCT
bracis-33554	58	32	$	$	SYM
bracis-33554	58	33	$	$	SYM
bracis-33554	58	34	\begin{aligned	\begin{aligne	VERB
bracis-33554	58	35	}	}	PUNCT
bracis-33554	58	36	u(v^\pi	u(v^\pi	NOUN
bracis-33554	58	37	)	)	PUNCT
bracis-33554	58	38	=	=	SYM
bracis-33554	58	39	u(v_{u}^{\pi	u(v_{u}^{\pi	NOUN
bracis-33554	58	40	}	}	PUNCT
bracis-33554	58	41	)	)	PUNCT
bracis-33554	58	42	.	.	PUNCT
bracis-33554	59	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	59	2	(	(	PUNCT
bracis-33554	59	3	6	6	NUM
bracis-33554	59	4	)	)	PUNCT
bracis-33554	59	5	a	a	DET
bracis-33554	59	6	positive	positive	ADJ
bracis-33554	59	7	risk	risk	NOUN
bracis-33554	59	8	factor	factor	NOUN
bracis-33554	59	9	\(\gamma	\(\gamma	NOUN
bracis-33554	59	10	\	\	NOUN
bracis-33554	59	11	)	)	PUNCT
bracis-33554	59	12	indicates	indicate	VERB
bracis-33554	59	13	risk	risk	NOUN
bracis-33554	59	14	aversion	aversion	NOUN
bracis-33554	59	15	and	and	CCONJ
bracis-33554	59	16	implies	imply	VERB
bracis-33554	59	17	\(v^\pi	\(v^\pi	NOUN
bracis-33554	59	18	_	_	PUNCT
bracis-33554	59	19	u	u	NOUN
bracis-33554	59	20	<	<	X
bracis-33554	59	21	v^\pi	v^\pi	X
bracis-33554	59	22	\	\	PROPN
bracis-33554	59	23	)	)	PUNCT
bracis-33554	59	24	,	,	PUNCT
bracis-33554	59	25	while	while	SCONJ
bracis-33554	59	26	a	a	DET
bracis-33554	59	27	negative	negative	ADJ
bracis-33554	59	28	factor	factor	NOUN
bracis-33554	59	29	indicates	indicate	VERB
bracis-33554	59	30	risk	risk	NOUN
bracis-33554	59	31	propensity	propensity	NOUN
bracis-33554	59	32	and	and	CCONJ
bracis-33554	59	33	implies	imply	VERB
bracis-33554	59	34	\(v^\pi	\(v^\pi	NOUN
bracis-33554	59	35	_	_	PUNCT
bracis-33554	59	36	u	u	X
bracis-33554	59	37	>	>	X
bracis-33554	59	38	v^\pi	v^\pi	NOUN
bracis-33554	59	39	\	\	PROPN
bracis-33554	59	40	)	)	PUNCT
bracis-33554	59	41	.	.	PUNCT
bracis-33554	60	1	the	the	DET
bracis-33554	60	2	utility	utility	NOUN
bracis-33554	60	3	function	function	NOUN
bracis-33554	60	4	applied	apply	VERB
bracis-33554	60	5	to	to	ADP
bracis-33554	60	6	\(v_{u}^{\pi	\(v_{u}^{\pi	NOUN
bracis-33554	60	7	}	}	PUNCT
bracis-33554	60	8	\	\	NOUN
bracis-33554	60	9	)	)	PUNCT
bracis-33554	60	10	is	be	AUX
bracis-33554	60	11	defined	define	VERB
bracis-33554	60	12	 	 	SPACE
bracis-33554	60	13	as	as	ADP
bracis-33554	60	14	$	$	SYM
bracis-33554	60	15	$	$	SYM
bracis-33554	60	16	\begin{aligned	\begin{aligne	VERB
bracis-33554	60	17	}	}	PUNCT
bracis-33554	60	18	{	{	PUNCT
bracis-33554	60	19	u^\pi	u^\pi	ADJ
bracis-33554	60	20	}	}	PUNCT
bracis-33554	60	21	=	=	SYM
bracis-33554	60	22	u(v_{u}^{\pi	u(v_{u}^{\pi	NOUN
bracis-33554	60	23	}	}	PUNCT
bracis-33554	60	24	)	)	PUNCT
bracis-33554	61	1	=	=	PUNCT
bracis-33554	61	2	-(\text	-(\text	PROPN
bracis-33554	61	3	{	{	PUNCT
bracis-33554	61	4	sgn	sgn	NOUN
bracis-33554	61	5	}	}	PUNCT
bracis-33554	61	6	\gamma	\gamma	NUM
bracis-33554	61	7	)	)	PUNCT
bracis-33554	61	8	e^{-\gamma	e^{-\gamma	PROPN
bracis-33554	61	9	{	{	PUNCT
bracis-33554	61	10	v_{u}^{\pi	v_{u}^{\pi	NOUN
bracis-33554	61	11	}	}	PUNCT
bracis-33554	61	12	}	}	PUNCT
bracis-33554	61	13	}	}	PUNCT
bracis-33554	61	14	.	.	PUNCT
bracis-33554	62	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	62	2	(	(	PUNCT
bracis-33554	62	3	7	7	NUM
bracis-33554	62	4	)	)	PUNCT
bracis-33554	62	5	the	the	DET
bracis-33554	62	6	utility	utility	NOUN
bracis-33554	62	7	of	of	ADP
bracis-33554	62	8	policy	policy	NOUN
bracis-33554	62	9	\(u^\pi	\(u^\pi	PUNCT
bracis-33554	62	10	\	\	NOUN
bracis-33554	62	11	)	)	PUNCT
bracis-33554	62	12	in	in	ADP
bracis-33554	62	13	iteration	iteration	NOUN
bracis-33554	62	14	\(n+1\	\(n+1\	NOUN
bracis-33554	62	15	)	)	PUNCT
bracis-33554	62	16	can	can	AUX
bracis-33554	62	17	be	be	AUX
bracis-33554	62	18	calculated	calculate	VERB
bracis-33554	62	19	by	by	ADP
bracis-33554	62	20	equation	equation	NOUN
bracis-33554	62	21	[	[	X
bracis-33554	62	22	2	2	X
bracis-33554	62	23	]	]	SYM
bracis-33554	62	24	$	$	SYM
bracis-33554	62	25	$	$	SYM
bracis-33554	62	26	\begin{aligned	\begin{aligne	VERB
bracis-33554	62	27	}	}	PUNCT
bracis-33554	62	28	{	{	PUNCT
bracis-33554	62	29	u^{\pi	u^{\pi	NOUN
bracis-33554	62	30	,	,	PUNCT
bracis-33554	62	31	n+1}(s	n+1}(s	PROPN
bracis-33554	62	32	)	)	PUNCT
bracis-33554	62	33	}	}	PUNCT
bracis-33554	62	34	=	=	SYM
bracis-33554	62	35	\sum	\sum	NOUN
bracis-33554	62	36	_	_	PUNCT
bracis-33554	62	37	{	{	PUNCT
bracis-33554	62	38	j\in	j\in	PROPN
bracis-33554	62	39	s	s	PART
bracis-33554	62	40	}	}	PUNCT
bracis-33554	62	41	p_\pi	p_\pi	NOUN
bracis-33554	62	42	^n(s	^n(	NOUN
bracis-33554	62	43	,	,	PUNCT
bracis-33554	62	44	j)e^{-\gamma	j)e^{-\gamma	PROPN
bracis-33554	62	45	r_\pi	r_\pi	NOUN
bracis-33554	62	46	(	(	PUNCT
bracis-33554	62	47	s)}{u^{\pi	s)}{u^{\pi	NOUN
bracis-33554	62	48	,	,	PUNCT
bracis-33554	62	49	n}(j	n}(j	NOUN
bracis-33554	62	50	)	)	PUNCT
bracis-33554	62	51	}	}	PUNCT
bracis-33554	62	52	,	,	PUNCT
bracis-33554	62	53	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	62	54	(	(	PUNCT
bracis-33554	62	55	8)	8)	NUM
bracis-33554	62	56	where	where	SCONJ
bracis-33554	62	57	\(u^{\pi	\(u^{\pi	NOUN
bracis-33554	62	58	,	,	PUNCT
bracis-33554	62	59	0	0	NUM
bracis-33554	62	60	}	}	PUNCT
bracis-33554	62	61	=	=	SYM
bracis-33554	62	62	(	(	PUNCT
bracis-33554	62	63	-1	-1	INTJ
bracis-33554	62	64	,	,	PUNCT
bracis-33554	62	65	...	...	PUNCT
bracis-33554	62	66	,	,	PUNCT
bracis-33554	62	67	-1)\	-1)\	NOUN
bracis-33554	62	68	)	)	PUNCT
bracis-33554	62	69	,	,	PUNCT
bracis-33554	62	70	\(|u^{\pi	\(|u^{\pi	NOUN
bracis-33554	62	71	,	,	PUNCT
bracis-33554	62	72	0}|	0}|	NUM
bracis-33554	62	73	=	=	SYM
bracis-33554	62	74	|s|\	|s|\	NOUN
bracis-33554	62	75	)	)	PUNCT
bracis-33554	62	76	e	e	NOUN
bracis-33554	62	77	\(p_\pi	\(p_\pi	X
bracis-33554	62	78	^0	^0	SYM
bracis-33554	62	79	=	=	SYM
bracis-33554	62	80	i\	i\	PROPN
bracis-33554	62	81	)	)	PUNCT
bracis-33554	62	82	.	.	PUNCT
bracis-33554	63	1	from	from	ADP
bracis-33554	63	2	\(u^{\pi	\(u^{\pi	ADJ
bracis-33554	63	3	,	,	PUNCT
bracis-33554	63	4	{	{	PUNCT
bracis-33554	63	5	n+1}}(s)\	n+1}}(s)\	NOUN
bracis-33554	63	6	)	)	PUNCT
bracis-33554	63	7	,	,	PUNCT
bracis-33554	63	8	the	the	DET
bracis-33554	63	9	certainty	certainty	NOUN
bracis-33554	63	10	equivalent	equivalent	NOUN
bracis-33554	63	11	can	can	AUX
bracis-33554	63	12	be	be	AUX
bracis-33554	63	13	calculated	calculate	VERB
bracis-33554	63	14	by	by	ADP
bracis-33554	63	15	\(v_{u}^{\pi	\(v_{u}^{\pi	NOUN
bracis-33554	63	16	,	,	PUNCT
bracis-33554	63	17	n}(s	n}(s	PROPN
bracis-33554	63	18	)	)	PUNCT
bracis-33554	64	1	=	=	SYM
bracis-33554	64	2	u^{-1}(u^{\pi	u^{-1}(u^{\pi	X
bracis-33554	64	3	,	,	PUNCT
bracis-33554	64	4	n}(s))\	n}(s))\	PROPN
bracis-33554	64	5	)	)	PUNCT
bracis-33554	64	6	.	.	PUNCT
bracis-33554	65	1	during	during	ADP
bracis-33554	65	2	the	the	DET
bracis-33554	65	3	process	process	NOUN
bracis-33554	65	4	,	,	PUNCT
bracis-33554	65	5	\(v_{u}^{\pi	\(v_{u}^{\pi	NOUN
bracis-33554	65	6	,	,	PUNCT
bracis-33554	65	7	n}\	n}\	PROPN
bracis-33554	65	8	)	)	PUNCT
bracis-33554	65	9	grows	grow	VERB
bracis-33554	65	10	linearly	linearly	ADV
bracis-33554	65	11	,	,	PUNCT
bracis-33554	65	12	and	and	CCONJ
bracis-33554	65	13	its	its	PRON
bracis-33554	65	14	variation	variation	NOUN
bracis-33554	65	15	is	be	AUX
bracis-33554	65	16	called	call	VERB
bracis-33554	65	17	the	the	DET
bracis-33554	65	18	certainty	certainty	NOUN
bracis-33554	65	19	equivalent	equivalent	ADJ
bracis-33554	65	20	gain	gain	NOUN
bracis-33554	65	21	,	,	PUNCT
bracis-33554	65	22	denoted	denote	VERB
bracis-33554	65	23	by	by	ADP
bracis-33554	65	24	\(g^\pi	\(g^\pi	NOUN
bracis-33554	65	25	_	_	PUNCT
bracis-33554	65	26	u\	u\	NOUN
bracis-33554	65	27	)	)	PUNCT
bracis-33554	65	28	.	.	PUNCT
bracis-33554	66	1	using	use	VERB
bracis-33554	66	2	the	the	DET
bracis-33554	66	3	exponential	exponential	ADJ
bracis-33554	66	4	utility	utility	NOUN
bracis-33554	66	5	criterion	criterion	NOUN
bracis-33554	66	6	,	,	PUNCT
bracis-33554	66	7	an	an	DET
bracis-33554	66	8	agent	agent	NOUN
bracis-33554	66	9	seeks	seek	VERB
bracis-33554	66	10	a	a	DET
bracis-33554	66	11	policy	policy	NOUN
bracis-33554	66	12	that	that	PRON
bracis-33554	66	13	maximizes	maximize	VERB
bracis-33554	66	14	the	the	DET
bracis-33554	66	15	certainty	certainty	NOUN
bracis-33554	66	16	equivalent	equivalent	ADJ
bracis-33554	66	17	gain	gain	NOUN
bracis-33554	66	18	of	of	ADP
bracis-33554	66	19	an	an	DET
bracis-33554	66	20	mdp	mdp	PROPN
bracis-33554	66	21	.	.	PUNCT
bracis-33554	67	1	howard	howard	PROPN
bracis-33554	67	2	and	and	CCONJ
bracis-33554	67	3	matheson	matheson	PROPN
bracis-33554	68	1	[	[	X
bracis-33554	68	2	2	2	NUM
bracis-33554	68	3	]	]	X
bracis-33554	68	4	propose	propose	VERB
bracis-33554	68	5	a	a	DET
bracis-33554	68	6	policy	policy	NOUN
bracis-33554	68	7	iteration	iteration	NOUN
bracis-33554	68	8	algorithm	algorithm	NOUN
bracis-33554	68	9	that	that	PRON
bracis-33554	68	10	finds	find	VERB
bracis-33554	68	11	a	a	DET
bracis-33554	68	12	stationary	stationary	ADJ
bracis-33554	68	13	policy	policy	NOUN
bracis-33554	68	14	and	and	CCONJ
bracis-33554	68	15	deals	deal	NOUN
bracis-33554	68	16	only	only	ADV
bracis-33554	68	17	with	with	ADP
bracis-33554	68	18	acyclic	acyclic	ADJ
bracis-33554	68	19	and	and	CCONJ
bracis-33554	68	20	irreducible	irreducible	ADJ
bracis-33554	68	21	markov	markov	NOUN
bracis-33554	68	22	processes	process	NOUN
bracis-33554	68	23	(	(	PUNCT
bracis-33554	68	24	all	all	DET
bracis-33554	68	25	states	state	NOUN
bracis-33554	68	26	communicate	communicate	VERB
bracis-33554	68	27	)	)	PUNCT
bracis-33554	68	28	.	.	PUNCT
bracis-33554	69	1	given	give	VERB
bracis-33554	69	2	an	an	DET
bracis-33554	69	3	arbitrary	arbitrary	ADJ
bracis-33554	69	4	initial	initial	ADJ
bracis-33554	69	5	policy	policy	NOUN
bracis-33554	69	6	,	,	PUNCT
bracis-33554	69	7	the	the	DET
bracis-33554	69	8	system	system	NOUN
bracis-33554	69	9	of	of	ADP
bracis-33554	69	10	eqs	eqs	PROPN
bracis-33554	69	11	.	.	PUNCT
bracis-33554	69	12	 	 	SPACE
bracis-33554	69	13	9	9	NUM
bracis-33554	69	14	must	must	AUX
bracis-33554	69	15	be	be	AUX
bracis-33554	69	16	solved	solve	VERB
bracis-33554	69	17	in	in	ADP
bracis-33554	69	18	the	the	DET
bracis-33554	69	19	policy	policy	NOUN
bracis-33554	69	20	evaluation	evaluation	NOUN
bracis-33554	69	21	step	step	NOUN
bracis-33554	69	22	to	to	PART
bracis-33554	69	23	find	find	VERB
bracis-33554	69	24	the	the	DET
bracis-33554	69	25	certainty	certainty	NOUN
bracis-33554	69	26	equivalent	equivalent	ADJ
bracis-33554	69	27	gain	gain	NOUN
bracis-33554	69	28	\(g_u^\pi	\(g_u^\pi	NOUN
bracis-33554	69	29	\	\	NOUN
bracis-33554	69	30	)	)	PUNCT
bracis-33554	69	31	and	and	CCONJ
bracis-33554	69	32	the	the	DET
bracis-33554	69	33	certainty	certainty	PROPN
bracis-33554	69	34	equivalents	equivalent	NOUN
bracis-33554	69	35	\(v_u^\pi	\(v_u^\pi	VERB
bracis-33554	69	36	\	\	NOUN
bracis-33554	69	37	)	)	PUNCT
bracis-33554	70	1	[	[	X
bracis-33554	70	2	2	2	X
bracis-33554	70	3	]	]	SYM
bracis-33554	70	4	$	$	SYM
bracis-33554	70	5	$	$	SYM
bracis-33554	70	6	\begin{aligned	\begin{aligne	VERB
bracis-33554	70	7	}	}	PUNCT
bracis-33554	70	8	e^{-\gamma	e^{-\gamma	X
bracis-33554	71	1	(	(	PUNCT
bracis-33554	71	2	g_u^\pi	g_u^\pi	NOUN
bracis-33554	71	3	+	+	PROPN
bracis-33554	71	4	v_u^\pi	v_u^\pi	PROPN
bracis-33554	71	5	(	(	PUNCT
bracis-33554	71	6	s	s	NOUN
bracis-33554	71	7	)	)	PUNCT
bracis-33554	71	8	)	)	PUNCT
bracis-33554	71	9	}	}	PUNCT
bracis-33554	72	1	=	=	X
bracis-33554	72	2	\sum	\sum	NOUN
bracis-33554	72	3	_	_	PUNCT
bracis-33554	72	4	{	{	PUNCT
bracis-33554	72	5	j\in	j\in	PROPN
bracis-33554	72	6	s	s	PART
bracis-33554	72	7	}	}	PUNCT
bracis-33554	72	8	p(j|s,\pi	p(j|s,\pi	NOUN
bracis-33554	72	9	(	(	PUNCT
bracis-33554	72	10	s))e^{-\gamma	s))e^{-\gamma	PROPN
bracis-33554	72	11	(	(	PUNCT
bracis-33554	72	12	r(s,\pi	r(s,\pi	NOUN
bracis-33554	72	13	(	(	PUNCT
bracis-33554	72	14	s))+v_u^\pi	s))+v_u^\pi	PROPN
bracis-33554	72	15	(	(	PUNCT
bracis-33554	72	16	j	j	NOUN
bracis-33554	72	17	)	)	PUNCT
bracis-33554	72	18	)	)	PUNCT
bracis-33554	72	19	}	}	PUNCT
bracis-33554	72	20	.	.	PUNCT
bracis-33554	73	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	73	2	(	(	PUNCT
bracis-33554	73	3	9	9	NUM
bracis-33554	73	4	)	)	PUNCT
bracis-33554	73	5	since	since	SCONJ
bracis-33554	73	6	there	there	PRON
bracis-33554	73	7	are	be	VERB
bracis-33554	73	8	more	more	ADJ
bracis-33554	73	9	variables	variable	NOUN
bracis-33554	73	10	than	than	ADP
bracis-33554	73	11	equations	equation	NOUN
bracis-33554	73	12	,	,	PUNCT
bracis-33554	73	13	one	one	NUM
bracis-33554	73	14	of	of	ADP
bracis-33554	73	15	the	the	DET
bracis-33554	73	16	certainty	certainty	ADJ
bracis-33554	73	17	equivalent	equivalent	ADJ
bracis-33554	73	18	values	value	NOUN
bracis-33554	73	19	must	must	AUX
bracis-33554	73	20	be	be	AUX
bracis-33554	73	21	set	set	VERB
bracis-33554	73	22	to	to	ADP
bracis-33554	73	23	0	0	NUM
bracis-33554	73	24	.	.	PUNCT
bracis-33554	74	1	then	then	ADV
bracis-33554	74	2	,	,	PUNCT
bracis-33554	74	3	using	use	VERB
bracis-33554	74	4	the	the	DET
bracis-33554	74	5	values	value	NOUN
bracis-33554	74	6	found	find	VERB
bracis-33554	74	7	in	in	ADP
bracis-33554	74	8	the	the	DET
bracis-33554	74	9	policy	policy	NOUN
bracis-33554	74	10	evaluation	evaluation	NOUN
bracis-33554	74	11	step	step	NOUN
bracis-33554	74	12	of	of	ADP
bracis-33554	74	13	the	the	DET
bracis-33554	74	14	previous	previous	ADJ
bracis-33554	74	15	policy	policy	NOUN
bracis-33554	74	16	,	,	PUNCT
bracis-33554	74	17	a	a	DET
bracis-33554	74	18	policy	policy	NOUN
bracis-33554	74	19	improvement	improvement	NOUN
bracis-33554	74	20	step	step	NOUN
bracis-33554	74	21	is	be	AUX
bracis-33554	74	22	applied	apply	VERB
bracis-33554	74	23	to	to	PART
bracis-33554	74	24	select	select	VERB
bracis-33554	74	25	,	,	PUNCT
bracis-33554	74	26	in	in	ADP
bracis-33554	74	27	each	each	DET
bracis-33554	74	28	state	state	NOUN
bracis-33554	74	29	s	s	PROPN
bracis-33554	74	30	,	,	PUNCT
bracis-33554	74	31	a	a	DET
bracis-33554	74	32	new	new	ADJ
bracis-33554	74	33	action	action	NOUN
bracis-33554	74	34	a	a	PRON
bracis-33554	74	35	that	that	PRON
bracis-33554	74	36	maximizes	maximize	VERB
bracis-33554	74	37	the	the	DET
bracis-33554	74	38	equation	equation	NOUN
bracis-33554	74	39	[	[	X
bracis-33554	74	40	2	2	X
bracis-33554	74	41	]	]	SYM
bracis-33554	74	42	$	$	SYM
bracis-33554	74	43	$	$	SYM
bracis-33554	74	44	\begin{aligned	\begin{aligne	VERB
bracis-33554	74	45	}	}	PUNCT
bracis-33554	74	46	v_u^\pi	v_u^\pi	X
bracis-33554	74	47	(	(	PUNCT
bracis-33554	74	48	s	s	PROPN
bracis-33554	74	49	,	,	PUNCT
bracis-33554	74	50	a	a	PRON
bracis-33554	74	51	)	)	PUNCT
bracis-33554	74	52	=	=	SYM
bracis-33554	74	53	\frac{1}{\gamma	\frac{1}{\gamma	PROPN
bracis-33554	74	54	}	}	PUNCT
bracis-33554	75	1	\text	\text	ADV
bracis-33554	75	2	{	{	PUNCT
bracis-33554	75	3	ln}\left	ln}\left	NOUN
bracis-33554	75	4	[	[	PUNCT
bracis-33554	75	5	\sum	\sum	NOUN
bracis-33554	75	6	_	_	PUNCT
bracis-33554	75	7	{	{	PUNCT
bracis-33554	75	8	j\in	j\in	PROPN
bracis-33554	75	9	s	s	PROPN
bracis-33554	75	10	}	}	PUNCT
bracis-33554	75	11	p(j|s	p(j|s	NUM
bracis-33554	75	12	,	,	PUNCT
bracis-33554	75	13	a)e^{-\gamma	a)e^{-\gamma	PROPN
bracis-33554	75	14	(	(	PUNCT
bracis-33554	75	15	r(s	r(s	PROPN
bracis-33554	75	16	,	,	PUNCT
bracis-33554	75	17	a)+v_u^\pi	a)+v_u^\pi	NOUN
bracis-33554	75	18	(	(	PUNCT
bracis-33554	75	19	j))}\right	j))}\right	NOUN
bracis-33554	75	20	]	]	PUNCT
bracis-33554	75	21	.	.	PUNCT
bracis-33554	76	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	76	2	(	(	PUNCT
bracis-33554	76	3	10	10	NUM
bracis-33554	76	4	)	)	PUNCT
bracis-33554	76	5	when	when	SCONJ
bracis-33554	76	6	no	no	DET
bracis-33554	76	7	change	change	NOUN
bracis-33554	76	8	occurs	occur	VERB
bracis-33554	76	9	in	in	ADP
bracis-33554	76	10	any	any	DET
bracis-33554	76	11	state	state	NOUN
bracis-33554	76	12	,	,	PUNCT
bracis-33554	76	13	the	the	DET
bracis-33554	76	14	optimal	optimal	ADJ
bracis-33554	76	15	policy	policy	NOUN
bracis-33554	76	16	has	have	AUX
bracis-33554	76	17	been	be	AUX
bracis-33554	76	18	found	find	VERB
bracis-33554	76	19	.	.	PUNCT
bracis-33554	77	1	2.3	2.3	NUM
bracis-33554	77	2	risk	risk	NOUN
bracis-33554	77	3	-	-	PUNCT
bracis-33554	77	4	sensitive	sensitive	ADJ
bracis-33554	77	5	criterion	criterion	NOUN
bracis-33554	77	6	with	with	ADP
bracis-33554	77	7	cvar	cvar	NOUN
bracis-33554	77	8	another	another	DET
bracis-33554	77	9	way	way	NOUN
bracis-33554	77	10	to	to	PART
bracis-33554	77	11	insert	insert	VERB
bracis-33554	77	12	risk	risk	NOUN
bracis-33554	77	13	into	into	ADP
bracis-33554	77	14	mdps	mdps	NOUN
bracis-33554	77	15	is	be	AUX
bracis-33554	77	16	through	through	ADP
bracis-33554	77	17	the	the	DET
bracis-33554	77	18	use	use	NOUN
bracis-33554	77	19	of	of	ADP
bracis-33554	77	20	var	var	NOUN
bracis-33554	77	21	and	and	CCONJ
bracis-33554	77	22	cvar	cvar	ADJ
bracis-33554	77	23	risk	risk	NOUN
bracis-33554	77	24	measures	measure	NOUN
bracis-33554	77	25	.	.	PUNCT
bracis-33554	78	1	the	the	DET
bracis-33554	78	2	var	var	NOUN
bracis-33554	78	3	(	(	PUNCT
bracis-33554	78	4	value	value	NOUN
bracis-33554	78	5	at	at	ADP
bracis-33554	78	6	risk	risk	NOUN
bracis-33554	78	7	)	)	PUNCT
bracis-33554	78	8	and	and	CCONJ
bracis-33554	78	9	cvar	cvar	NOUN
bracis-33554	78	10	(	(	PUNCT
bracis-33554	78	11	conditional	conditional	ADJ
bracis-33554	78	12	-	-	PUNCT
bracis-33554	78	13	value	value	NOUN
bracis-33554	78	14	-	-	PUNCT
bracis-33554	78	15	at	at	ADP
bracis-33554	78	16	-	-	PUNCT
bracis-33554	78	17	risk	risk	NOUN
bracis-33554	78	18	)	)	PUNCT
bracis-33554	78	19	metrics	metric	NOUN
bracis-33554	78	20	are	be	AUX
bracis-33554	78	21	widely	widely	ADV
bracis-33554	78	22	used	use	VERB
bracis-33554	78	23	for	for	ADP
bracis-33554	78	24	portfolio	portfolio	NOUN
bracis-33554	78	25	management	management	NOUN
bracis-33554	78	26	of	of	ADP
bracis-33554	78	27	financial	financial	ADJ
bracis-33554	78	28	assets	asset	NOUN
bracis-33554	78	29	.	.	PUNCT
bracis-33554	79	1	var	var	NOUN
bracis-33554	79	2	measures	measure	NOUN
bracis-33554	79	3	the	the	DET
bracis-33554	79	4	worst	bad	ADJ
bracis-33554	79	5	expected	expect	VERB
bracis-33554	79	6	loss	loss	NOUN
bracis-33554	79	7	within	within	ADP
bracis-33554	79	8	a	a	DET
bracis-33554	79	9	given	give	VERB
bracis-33554	79	10	\	\	PROPN
bracis-33554	79	11	(	(	PUNCT
bracis-33554	79	12	\alpha	\alpha	ADJ
bracis-33554	79	13	\	\	ADJ
bracis-33554	79	14	)	)	PUNCT
bracis-33554	79	15	confidence	confidence	NOUN
bracis-33554	79	16	level	level	NOUN
bracis-33554	79	17	,	,	PUNCT
bracis-33554	79	18	where	where	SCONJ
bracis-33554	79	19	\(\alpha	\(\alpha	NOUN
bracis-33554	79	20	\in	\in	PROPN
bracis-33554	79	21	(	(	PUNCT
bracis-33554	79	22	0	0	NUM
bracis-33554	79	23	,	,	PUNCT
bracis-33554	79	24	1)\	1)\	NUM
bracis-33554	79	25	)	)	PUNCT
bracis-33554	79	26	.	.	PUNCT
bracis-33554	80	1	var	var	PROPN
bracis-33554	80	2	is	be	AUX
bracis-33554	80	3	defined	define	VERB
bracis-33554	80	4	as	as	ADP
bracis-33554	80	5	the	the	DET
bracis-33554	80	6	\	\	NOUN
bracis-33554	80	7	(	(	PUNCT
bracis-33554	80	8	1\alpha	1\alpha	NUM
bracis-33554	80	9	\	\	NOUN
bracis-33554	80	10	)	)	PUNCT
bracis-33554	80	11	quantile	quantile	NOUN
bracis-33554	80	12	of	of	ADP
bracis-33554	80	13	z	z	PROPN
bracis-33554	80	14	,	,	PUNCT
bracis-33554	80	15	i.e.	i.e.	X
bracis-33554	80	16	$	$	SYM
bracis-33554	80	17	$	$	SYM
bracis-33554	80	18	\begin{aligned	\begin{aligne	VERB
bracis-33554	80	19	}	}	PUNCT
bracis-33554	80	20	\text	\text	ADP
bracis-33554	80	21	{	{	PUNCT
bracis-33554	80	22	var}_\alpha	var}_\alpha	PROPN
bracis-33554	80	23	(	(	PUNCT
bracis-33554	80	24	z	z	NOUN
bracis-33554	80	25	)	)	PUNCT
bracis-33554	80	26	=	=	SYM
bracis-33554	80	27	\min	\min	NOUN
bracis-33554	80	28	\	\	PROPN
bracis-33554	80	29	{	{	PUNCT
bracis-33554	80	30	z	z	NOUN
bracis-33554	80	31	|	|	ADV
bracis-33554	80	32	f(z	f(z	PROPN
bracis-33554	80	33	)	)	PUNCT
bracis-33554	80	34	\ge	\ge	PROPN
bracis-33554	80	35	1-\alpha	1-\alpha	NUM
bracis-33554	80	36	\	\	PROPN
bracis-33554	80	37	}	}	PUNCT
bracis-33554	80	38	,	,	PUNCT
bracis-33554	80	39	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	80	40	(	(	PUNCT
bracis-33554	80	41	11	11	NUM
bracis-33554	80	42	)	)	PUNCT
bracis-33554	80	43	where	where	SCONJ
bracis-33554	80	44	z	z	NOUN
bracis-33554	80	45	is	be	AUX
bracis-33554	80	46	a	a	DET
bracis-33554	80	47	random	random	ADJ
bracis-33554	80	48	variable	variable	NOUN
bracis-33554	80	49	and	and	CCONJ
bracis-33554	80	50	f(z	f(z	PROPN
bracis-33554	80	51	)	)	PUNCT
bracis-33554	80	52	is	be	AUX
bracis-33554	80	53	the	the	DET
bracis-33554	80	54	cumulative	cumulative	ADJ
bracis-33554	80	55	distribution	distribution	NOUN
bracis-33554	80	56	function	function	NOUN
bracis-33554	80	57	.	.	PUNCT
bracis-33554	81	1	an	an	DET
bracis-33554	81	2	alternative	alternative	ADJ
bracis-33554	81	3	measure	measure	NOUN
bracis-33554	81	4	is	be	AUX
bracis-33554	81	5	the	the	DET
bracis-33554	81	6	cvar	cvar	PROPN
bracis-33554	81	7	metric	metric	NOUN
bracis-33554	81	8	,	,	PUNCT
bracis-33554	81	9	a	a	DET
bracis-33554	81	10	coherent	coherent	ADJ
bracis-33554	81	11	risk	risk	NOUN
bracis-33554	81	12	measure	measure	NOUN
bracis-33554	81	13	[	[	X
bracis-33554	81	14	6	6	NUM
bracis-33554	81	15	]	]	PUNCT
bracis-33554	81	16	,	,	PUNCT
bracis-33554	81	17	that	that	PRON
bracis-33554	81	18	is	be	AUX
bracis-33554	81	19	computed	compute	VERB
bracis-33554	81	20	by	by	ADP
bracis-33554	81	21	averaging	average	VERB
bracis-33554	81	22	losses	loss	NOUN
bracis-33554	81	23	that	that	PRON
bracis-33554	81	24	exceed	exceed	VERB
bracis-33554	81	25	the	the	DET
bracis-33554	81	26	var	var	NOUN
bracis-33554	81	27	value	value	NOUN
bracis-33554	81	28	.	.	PUNCT
bracis-33554	82	1	cvar	cvar	PROPN
bracis-33554	82	2	,	,	PUNCT
bracis-33554	82	3	with	with	ADP
bracis-33554	82	4	a	a	DET
bracis-33554	82	5	confidence	confidence	NOUN
bracis-33554	82	6	level	level	NOUN
bracis-33554	82	7	\(\alpha	\(\alpha	X
bracis-33554	82	8	\in	\in	PROPN
bracis-33554	82	9	(	(	PUNCT
bracis-33554	82	10	0	0	NUM
bracis-33554	82	11	,	,	PUNCT
bracis-33554	82	12	1)\	1)\	NUM
bracis-33554	82	13	)	)	PUNCT
bracis-33554	82	14	is	be	AUX
bracis-33554	82	15	defined	define	VERB
bracis-33554	82	16	as	as	ADP
bracis-33554	82	17	[	[	X
bracis-33554	82	18	5	5	NUM
bracis-33554	82	19	]	]	SYM
bracis-33554	82	20	$	$	SYM
bracis-33554	82	21	$	$	SYM
bracis-33554	82	22	\begin{aligned	\begin{aligne	VERB
bracis-33554	82	23	}	}	PUNCT
bracis-33554	82	24	\text	\text	ADP
bracis-33554	82	25	{	{	PUNCT
bracis-33554	82	26	cvar}_\alpha	cvar}_\alpha	PROPN
bracis-33554	82	27	(	(	PUNCT
bracis-33554	82	28	z	z	NOUN
bracis-33554	82	29	)	)	PUNCT
bracis-33554	82	30	=	=	VERB
bracis-33554	83	1	\min	\min	NOUN
bracis-33554	83	2	_	_	PUNCT
bracis-33554	83	3	{	{	PUNCT
bracis-33554	83	4	w\in	w\in	X
bracis-33554	83	5	\mathbb	\mathbb	PROPN
bracis-33554	83	6	{	{	PUNCT
bracis-33554	83	7	r	r	NOUN
bracis-33554	83	8	}	}	PUNCT
bracis-33554	83	9	}	}	PUNCT
bracis-33554	83	10	\left\	\left\	PROPN
bracis-33554	83	11	{	{	PUNCT
bracis-33554	83	12	{	{	PUNCT
bracis-33554	83	13	w	w	PROPN
bracis-33554	83	14	+	+	CCONJ
bracis-33554	83	15	\frac{1}{\alpha	\frac{1}{\alpha	PROPN
bracis-33554	83	16	}	}	PUNCT
bracis-33554	83	17	e\left	e\left	VERB
bracis-33554	83	18	[	[	PUNCT
bracis-33554	83	19	{	{	PUNCT
bracis-33554	83	20	(	(	PUNCT
bracis-33554	83	21	z	z	NOUN
bracis-33554	83	22	-	-	PUNCT
bracis-33554	83	23	w)^{+	w)^{+	NOUN
bracis-33554	83	24	}	}	PUNCT
bracis-33554	83	25	}	}	PUNCT
bracis-33554	83	26	_	_	PRON
bracis-33554	83	27	{	{	PUNCT
bracis-33554	83	28	}	}	PUNCT
bracis-33554	83	29	\,\right	\,\right	PROPN
bracis-33554	83	30	]	]	PUNCT
bracis-33554	83	31	}	}	PUNCT
bracis-33554	83	32	_	_	PUNCT
bracis-33554	83	33	{	{	PUNCT
bracis-33554	83	34	}	}	PUNCT
bracis-33554	83	35	\,\right\	\,\right\	ADJ
bracis-33554	83	36	}	}	PUNCT
bracis-33554	83	37	,	,	PUNCT
bracis-33554	83	38	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	83	39	(	(	PUNCT
bracis-33554	83	40	12	12	NUM
bracis-33554	83	41	)	)	PUNCT
bracis-33554	83	42	where	where	SCONJ
bracis-33554	83	43	\((x)^{+}\	\((x)^{+}\	NOUN
bracis-33554	83	44	)	)	PUNCT
bracis-33554	83	45	=	=	SYM
bracis-33554	83	46	max\(\{x,0\}\	max\(\{x,0\}\	X
bracis-33554	83	47	)	)	PUNCT
bracis-33554	83	48	represents	represent	VERB
bracis-33554	83	49	the	the	DET
bracis-33554	83	50	positive	positive	ADJ
bracis-33554	83	51	part	part	NOUN
bracis-33554	83	52	of	of	ADP
bracis-33554	83	53	x	x	NOUN
bracis-33554	83	54	,	,	PUNCT
bracis-33554	83	55	and	and	CCONJ
bracis-33554	83	56	w	w	NOUN
bracis-33554	83	57	represents	represent	VERB
bracis-33554	83	58	the	the	DET
bracis-33554	83	59	decision	decision	NOUN
bracis-33554	83	60	variable	variable	NOUN
bracis-33554	83	61	that	that	SCONJ
bracis-33554	83	62	,	,	PUNCT
bracis-33554	83	63	at	at	ADP
bracis-33554	83	64	the	the	DET
bracis-33554	83	65	optimum	optimum	ADJ
bracis-33554	83	66	point	point	NOUN
bracis-33554	83	67	,	,	PUNCT
bracis-33554	83	68	reaches	reach	VERB
bracis-33554	83	69	the	the	DET
bracis-33554	83	70	value	value	NOUN
bracis-33554	83	71	of	of	ADP
bracis-33554	83	72	 	 	SPACE
bracis-33554	83	73	var	var	NOUN
bracis-33554	83	74	$	$	SYM
bracis-33554	83	75	$	$	SYM
bracis-33554	83	76	\begin{aligned	\begin{aligne	VERB
bracis-33554	83	77	}	}	PUNCT
bracis-33554	83	78	\text	\text	ADP
bracis-33554	83	79	{	{	PUNCT
bracis-33554	83	80	cvar}_\alpha	cvar}_\alpha	PROPN
bracis-33554	83	81	(	(	PUNCT
bracis-33554	83	82	z	z	NOUN
bracis-33554	83	83	)	)	PUNCT
bracis-33554	84	1	=	=	PUNCT
bracis-33554	84	2	\text	\text	NOUN
bracis-33554	84	3	{	{	PUNCT
bracis-33554	84	4	var}_\alpha	var}_\alpha	PROPN
bracis-33554	84	5	(	(	PUNCT
bracis-33554	84	6	z	z	NOUN
bracis-33554	84	7	)	)	PUNCT
bracis-33554	84	8	+	+	CCONJ
bracis-33554	85	1	\frac{1}{\alpha	\frac{1}{\alpha	PROPN
bracis-33554	85	2	}	}	PUNCT
bracis-33554	85	3	e\left	e\left	VERB
bracis-33554	85	4	[	[	PUNCT
bracis-33554	85	5	{	{	PUNCT
bracis-33554	85	6	(	(	PUNCT
bracis-33554	85	7	z-\text	z-\text	NUM
bracis-33554	85	8	{	{	PUNCT
bracis-33554	85	9	var}_\alpha	var}_\alpha	PROPN
bracis-33554	85	10	(	(	PUNCT
bracis-33554	85	11	z))^{+	z))^{+	NOUN
bracis-33554	85	12	}	}	PUNCT
bracis-33554	85	13	}	}	PUNCT
bracis-33554	85	14	_	_	PRON
bracis-33554	85	15	{	{	PUNCT
bracis-33554	85	16	}	}	PUNCT
bracis-33554	85	17	\,\right	\,\right	PROPN
bracis-33554	85	18	]	]	PUNCT
bracis-33554	85	19	.	.	PUNCT
bracis-33554	86	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	86	2	(	(	PUNCT
bracis-33554	86	3	13	13	NUM
bracis-33554	86	4	)	)	PUNCT
bracis-33554	86	5	mdps	mdps	NOUN
bracis-33554	86	6	with	with	ADP
bracis-33554	86	7	the	the	DET
bracis-33554	86	8	cvar	cvar	NOUN
bracis-33554	86	9	criterion	criterion	NOUN
bracis-33554	86	10	for	for	ADP
bracis-33554	86	11	average	average	ADJ
bracis-33554	86	12	reward	reward	NOUN
bracis-33554	86	13	were	be	AUX
bracis-33554	86	14	studied	study	VERB
bracis-33554	86	15	for	for	ADP
bracis-33554	86	16	the	the	DET
bracis-33554	86	17	first	first	ADJ
bracis-33554	86	18	time	time	NOUN
bracis-33554	86	19	by	by	ADP
bracis-33554	86	20	xia	xia	PROPN
bracis-33554	86	21	and	and	CCONJ
bracis-33554	86	22	glynn	glynn	PROPN
bracis-33554	87	1	[	[	X
bracis-33554	87	2	7	7	NUM
bracis-33554	87	3	]	]	PUNCT
bracis-33554	87	4	.	.	PUNCT
bracis-33554	88	1	however	however	ADV
bracis-33554	88	2	,	,	PUNCT
bracis-33554	88	3	they	they	PRON
bracis-33554	88	4	only	only	ADV
bracis-33554	88	5	deal	deal	VERB
bracis-33554	88	6	with	with	ADP
bracis-33554	88	7	stationary	stationary	ADJ
bracis-33554	88	8	policies	policy	NOUN
bracis-33554	88	9	associated	associate	VERB
bracis-33554	88	10	with	with	ADP
bracis-33554	88	11	ergodic	ergodic	ADJ
bracis-33554	88	12	markov	markov	NOUN
bracis-33554	88	13	chains	chain	NOUN
bracis-33554	88	14	,	,	PUNCT
bracis-33554	88	15	and	and	CCONJ
bracis-33554	88	16	they	they	PRON
bracis-33554	88	17	suggest	suggest	VERB
bracis-33554	88	18	that	that	SCONJ
bracis-33554	88	19	the	the	DET
bracis-33554	88	20	results	result	NOUN
bracis-33554	88	21	can	can	AUX
bracis-33554	88	22	be	be	AUX
bracis-33554	88	23	extended	extend	VERB
bracis-33554	88	24	to	to	PART
bracis-33554	88	25	unichain	unichain	VERB
bracis-33554	88	26	mdps	mdps	PROPN
bracis-33554	88	27	.	.	PUNCT
bracis-33554	89	1	the	the	DET
bracis-33554	89	2	cvar	cvar	PROPN
bracis-33554	89	3	gain	gain	NOUN
bracis-33554	89	4	is	be	AUX
bracis-33554	89	5	defined	define	VERB
bracis-33554	89	6	as	as	ADP
bracis-33554	89	7	[	[	X
bracis-33554	89	8	7	7	NUM
bracis-33554	89	9	]	]	SYM
bracis-33554	89	10	$	$	SYM
bracis-33554	89	11	$	$	SYM
bracis-33554	89	12	\begin{aligned	\begin{aligne	VERB
bracis-33554	89	13	}	}	PUNCT
bracis-33554	89	14	g^\pi	g^\pi	VERB
bracis-33554	89	15	_	_	PRON
bracis-33554	89	16	{	{	PUNCT
bracis-33554	89	17	\text	\text	ADJ
bracis-33554	89	18	{	{	PUNCT
bracis-33554	89	19	cvar}_\alpha	cvar}_\alpha	NOUN
bracis-33554	89	20	}	}	PUNCT
bracis-33554	89	21	=	=	PUNCT
bracis-33554	89	22	\lim	\lim	NOUN
bracis-33554	89	23	_	_	PUNCT
bracis-33554	90	1	{	{	PUNCT
bracis-33554	90	2	n\rightarrow	n\rightarrow	NOUN
bracis-33554	90	3	\infty	\infty	PROPN
bracis-33554	90	4	}	}	PUNCT
bracis-33554	90	5	\frac{1}{n	\frac{1}{n	NOUN
bracis-33554	90	6	}	}	PUNCT
bracis-33554	90	7	\sum	\sum	NOUN
bracis-33554	90	8	_	_	PUNCT
bracis-33554	90	9	{	{	PUNCT
bracis-33554	90	10	n=1}^{n	n=1}^{n	ADV
bracis-33554	90	11	}	}	PUNCT
bracis-33554	90	12	\text	\text	ADV
bracis-33554	90	13	{	{	PUNCT
bracis-33554	90	14	cvar}_\alpha	cvar}_\alpha	PROPN
bracis-33554	90	15	(	(	PUNCT
bracis-33554	90	16	r_{n	r_{n	PROPN
bracis-33554	90	17	}	}	PUNCT
bracis-33554	90	18	)	)	PUNCT
bracis-33554	90	19	.	.	PUNCT
bracis-33554	91	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	91	2	(	(	PUNCT
bracis-33554	91	3	14	14	NUM
bracis-33554	91	4	)	)	PUNCT
bracis-33554	91	5	note	note	VERB
bracis-33554	91	6	that	that	SCONJ
bracis-33554	91	7	in	in	ADP
bracis-33554	91	8	eq	eq	ADP
bracis-33554	91	9	.	.	PUNCT
bracis-33554	91	10	 	 	SPACE
bracis-33554	91	11	14	14	NUM
bracis-33554	91	12	,	,	PUNCT
bracis-33554	91	13	the	the	DET
bracis-33554	91	14	random	random	ADJ
bracis-33554	91	15	variable	variable	NOUN
bracis-33554	91	16	is	be	AUX
bracis-33554	91	17	only	only	ADV
bracis-33554	91	18	the	the	DET
bracis-33554	91	19	immediate	immediate	ADJ
bracis-33554	91	20	reward	reward	NOUN
bracis-33554	91	21	.	.	PUNCT
bracis-33554	92	1	additionally	additionally	ADV
bracis-33554	92	2	,	,	PUNCT
bracis-33554	92	3	a	a	DET
bracis-33554	92	4	local	local	ADJ
bracis-33554	92	5	optimality	optimality	NOUN
bracis-33554	92	6	equation	equation	NOUN
bracis-33554	92	7	of	of	ADP
bracis-33554	92	8	bellman	bellman	NOUN
bracis-33554	92	9	is	be	AUX
bracis-33554	92	10	proposed	propose	VERB
bracis-33554	92	11	,	,	PUNCT
bracis-33554	92	12	and	and	CCONJ
bracis-33554	92	13	a	a	DET
bracis-33554	92	14	policy	policy	NOUN
bracis-33554	92	15	iteration	iteration	NOUN
bracis-33554	92	16	-	-	PUNCT
bracis-33554	92	17	type	type	NOUN
bracis-33554	92	18	algorithm	algorithm	NOUN
bracis-33554	92	19	is	be	AUX
bracis-33554	92	20	developed	develop	VERB
bracis-33554	92	21	.	.	PUNCT
bracis-33554	93	1	3	3	NUM
bracis-33554	93	2	a	a	DET
bracis-33554	93	3	unified	unified	ADJ
bracis-33554	93	4	framework	framework	NOUN
bracis-33554	93	5	in	in	ADP
bracis-33554	93	6	this	this	DET
bracis-33554	93	7	work	work	NOUN
bracis-33554	93	8	,	,	PUNCT
bracis-33554	93	9	some	some	DET
bracis-33554	93	10	interpretations	interpretation	NOUN
bracis-33554	93	11	of	of	ADP
bracis-33554	93	12	the	the	DET
bracis-33554	93	13	risk	risk	NOUN
bracis-33554	93	14	-	-	PUNCT
bracis-33554	93	15	neutral	neutral	ADJ
bracis-33554	93	16	average	average	ADJ
bracis-33554	93	17	reward	reward	NOUN
bracis-33554	93	18	criterion	criterion	NOUN
bracis-33554	93	19	are	be	AUX
bracis-33554	93	20	considered	consider	VERB
bracis-33554	93	21	,	,	PUNCT
bracis-33554	93	22	followed	follow	VERB
bracis-33554	93	23	by	by	ADP
bracis-33554	93	24	interpretations	interpretation	NOUN
bracis-33554	93	25	of	of	ADP
bracis-33554	93	26	the	the	DET
bracis-33554	93	27	risk	risk	NOUN
bracis-33554	93	28	-	-	PUNCT
bracis-33554	93	29	sensitive	sensitive	ADJ
bracis-33554	93	30	average	average	ADJ
bracis-33554	93	31	reward	reward	NOUN
bracis-33554	93	32	criterion	criterion	NOUN
bracis-33554	93	33	with	with	ADP
bracis-33554	93	34	utility	utility	NOUN
bracis-33554	93	35	function	function	NOUN
bracis-33554	93	36	and	and	CCONJ
bracis-33554	93	37	cvar	cvar	NOUN
bracis-33554	93	38	.	.	PUNCT
bracis-33554	94	1	the	the	DET
bracis-33554	94	2	proposed	propose	VERB
bracis-33554	94	3	framework	framework	NOUN
bracis-33554	94	4	considers	consider	VERB
bracis-33554	94	5	stationary	stationary	ADJ
bracis-33554	94	6	and	and	CCONJ
bracis-33554	94	7	aperiodic	aperiodic	ADJ
bracis-33554	94	8	policies	policy	NOUN
bracis-33554	94	9	,	,	PUNCT
bracis-33554	94	10	i.e.	i.e.	X
bracis-33554	94	11	,	,	PUNCT
bracis-33554	94	12	stationary	stationary	ADJ
bracis-33554	94	13	policies	policy	NOUN
bracis-33554	94	14	that	that	PRON
bracis-33554	94	15	generate	generate	VERB
bracis-33554	94	16	aperiodic	aperiodic	ADJ
bracis-33554	94	17	unichain	unichain	NOUN
bracis-33554	94	18	or	or	CCONJ
bracis-33554	94	19	aperiodic	aperiodic	ADJ
bracis-33554	94	20	multichain	multichain	NOUN
bracis-33554	94	21	markov	markov	NOUN
bracis-33554	94	22	chains	chain	NOUN
bracis-33554	94	23	.	.	PUNCT
bracis-33554	95	1	for	for	ADP
bracis-33554	95	2	aperiodic	aperiodic	ADJ
bracis-33554	95	3	policies	policy	NOUN
bracis-33554	95	4	\(p^*_\pi	\(p^*_\pi	VERB
bracis-33554	95	5	=	=	NOUN
bracis-33554	95	6	\lim	\lim	NOUN
bracis-33554	95	7	_	_	NOUN
bracis-33554	95	8	{	{	PUNCT
bracis-33554	95	9	n	n	CCONJ
bracis-33554	95	10	\rightarrow	\rightarrow	PROPN
bracis-33554	95	11	\infty	\infty	PROPN
bracis-33554	95	12	}	}	PUNCT
bracis-33554	95	13	p^n_\pi	p^n_\pi	PROPN
bracis-33554	95	14	\	\	NOUN
bracis-33554	95	15	)	)	PUNCT
bracis-33554	95	16	exists	exist	VERB
bracis-33554	95	17	.	.	PUNCT
bracis-33554	96	1	3.1	3.1	NUM
bracis-33554	96	2	formalization	formalization	NOUN
bracis-33554	96	3	of	of	ADP
bracis-33554	96	4	the	the	DET
bracis-33554	96	5	risk	risk	NOUN
bracis-33554	96	6	-	-	PUNCT
bracis-33554	96	7	neutral	neutral	ADJ
bracis-33554	96	8	criterion	criterion	NOUN
bracis-33554	96	9	one	one	NUM
bracis-33554	96	10	of	of	ADP
bracis-33554	96	11	the	the	DET
bracis-33554	96	12	most	most	ADV
bracis-33554	96	13	common	common	ADJ
bracis-33554	96	14	ways	way	NOUN
bracis-33554	96	15	to	to	PART
bracis-33554	96	16	calculate	calculate	VERB
bracis-33554	96	17	the	the	DET
bracis-33554	96	18	value	value	NOUN
bracis-33554	96	19	function	function	NOUN
bracis-33554	96	20	for	for	ADP
bracis-33554	96	21	mdps	mdps	NOUN
bracis-33554	96	22	is	be	AUX
bracis-33554	96	23	by	by	ADP
bracis-33554	96	24	computing	compute	VERB
bracis-33554	96	25	the	the	DET
bracis-33554	96	26	accumulated	accumulate	VERB
bracis-33554	96	27	reward	reward	NOUN
bracis-33554	96	28	.	.	PUNCT
bracis-33554	97	1	this	this	DET
bracis-33554	97	2	approach	approach	NOUN
bracis-33554	97	3	can	can	AUX
bracis-33554	97	4	be	be	AUX
bracis-33554	97	5	extended	extend	VERB
bracis-33554	97	6	to	to	AUX
bracis-33554	97	7	infinite	infinite	VERB
bracis-33554	97	8	horizon	horizon	NOUN
bracis-33554	97	9	,	,	PUNCT
bracis-33554	97	10	where	where	SCONJ
bracis-33554	97	11	to	to	PART
bracis-33554	97	12	ensure	ensure	VERB
bracis-33554	97	13	convergence	convergence	NOUN
bracis-33554	97	14	of	of	ADP
bracis-33554	97	15	the	the	DET
bracis-33554	97	16	value	value	NOUN
bracis-33554	97	17	,	,	PUNCT
bracis-33554	97	18	it	it	PRON
bracis-33554	97	19	is	be	AUX
bracis-33554	97	20	divided	divide	VERB
bracis-33554	97	21	by	by	ADP
bracis-33554	97	22	the	the	DET
bracis-33554	97	23	number	number	NOUN
bracis-33554	97	24	of	of	ADP
bracis-33554	97	25	decision	decision	NOUN
bracis-33554	97	26	steps	step	NOUN
bracis-33554	97	27	n	n	PRON
bracis-33554	97	28	(	(	PUNCT
bracis-33554	97	29	eq	eq	NOUN
bracis-33554	97	30	.	.	PUNCT
bracis-33554	97	31	 	 	SPACE
bracis-33554	97	32	15	15	NUM
bracis-33554	97	33	)	)	PUNCT
bracis-33554	97	34	.	.	PUNCT
bracis-33554	98	1	note	note	VERB
bracis-33554	98	2	that	that	SCONJ
bracis-33554	98	3	in	in	ADP
bracis-33554	98	4	this	this	DET
bracis-33554	98	5	equation	equation	NOUN
bracis-33554	98	6	,	,	PUNCT
bracis-33554	98	7	the	the	DET
bracis-33554	98	8	accumulated	accumulate	VERB
bracis-33554	98	9	reward	reward	NOUN
bracis-33554	98	10	is	be	AUX
bracis-33554	98	11	the	the	DET
bracis-33554	98	12	random	random	ADJ
bracis-33554	98	13	variable	variable	NOUN
bracis-33554	98	14	.	.	PUNCT
bracis-33554	99	1	from	from	ADP
bracis-33554	99	2	this	this	DET
bracis-33554	99	3	equation	equation	NOUN
bracis-33554	99	4	,	,	PUNCT
bracis-33554	99	5	various	various	ADJ
bracis-33554	99	6	interpretations	interpretation	NOUN
bracis-33554	99	7	of	of	ADP
bracis-33554	99	8	the	the	DET
bracis-33554	99	9	gain	gain	NOUN
bracis-33554	99	10	of	of	ADP
bracis-33554	99	11	an	an	DET
bracis-33554	99	12	mdp	mdp	NOUN
bracis-33554	99	13	for	for	ADP
bracis-33554	99	14	a	a	DET
bracis-33554	99	15	policy	policy	NOUN
bracis-33554	99	16	\(\pi	\(\pi	ADP
bracis-33554	99	17	\	\	NOUN
bracis-33554	99	18	)	)	PUNCT
bracis-33554	99	19	can	can	AUX
bracis-33554	99	20	be	be	AUX
bracis-33554	99	21	derived	derive	VERB
bracis-33554	99	22	.	.	PUNCT
bracis-33554	100	1	the	the	DET
bracis-33554	100	2	relationships	relationship	NOUN
bracis-33554	100	3	between	between	ADP
bracis-33554	100	4	these	these	DET
bracis-33554	100	5	interpretations	interpretation	NOUN
bracis-33554	100	6	are	be	AUX
bracis-33554	100	7	shown	show	VERB
bracis-33554	100	8	in	in	ADP
bracis-33554	100	9	eqs	eqs	PROPN
bracis-33554	100	10	.	.	PUNCT
bracis-33554	100	11	 	 	SPACE
bracis-33554	100	12	15	15	NUM
bracis-33554	100	13	to	to	PART
bracis-33554	100	14	18	18	NUM
bracis-33554	100	15	.	.	PUNCT
bracis-33554	101	1	$	$	SYM
bracis-33554	101	2	$	$	SYM
bracis-33554	101	3	\begin{aligned	\begin{aligne	VERB
bracis-33554	101	4	}	}	PUNCT
bracis-33554	101	5	g^\pi	g^\pi	PROPN
bracis-33554	101	6	&	&	CCONJ
bracis-33554	101	7	=	=	PROPN
bracis-33554	101	8	\lim	\lim	PROPN
bracis-33554	101	9	_	_	PUNCT
bracis-33554	101	10	{	{	PUNCT
bracis-33554	101	11	n\rightarrow	n\rightarrow	NOUN
bracis-33554	101	12	\infty	\infty	PROPN
bracis-33554	101	13	}	}	PUNCT
bracis-33554	101	14	\frac{1}{n	\frac{1}{n	NOUN
bracis-33554	101	15	}	}	PUNCT
bracis-33554	101	16	e\left	e\left	VERB
bracis-33554	101	17	[	[	PUNCT
bracis-33554	101	18	\sum	\sum	NOUN
bracis-33554	101	19	_	_	PUNCT
bracis-33554	101	20	{	{	PUNCT
bracis-33554	101	21	n=1}^{n	n=1}^{n	ADJ
bracis-33554	101	22	}	}	PUNCT
bracis-33554	101	23	r_{n	r_{n	PROPN
bracis-33554	101	24	}	}	PUNCT
bracis-33554	101	25	\right	\right	PROPN
bracis-33554	101	26	]	]	X
bracis-33554	101	27	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	101	28	(	(	PUNCT
bracis-33554	101	29	15	15	NUM
bracis-33554	101	30	)	)	PUNCT
bracis-33554	101	31	$	$	SYM
bracis-33554	101	32	$	$	SYM
bracis-33554	101	33	\begin{aligned	\begin{aligne	VERB
bracis-33554	101	34	}	}	PUNCT
bracis-33554	101	35	&	&	CCONJ
bracis-33554	101	36	=	=	SYM
bracis-33554	101	37	\lim	\lim	PROPN
bracis-33554	101	38	_	_	PUNCT
bracis-33554	101	39	{	{	PUNCT
bracis-33554	101	40	n\rightarrow	n\rightarrow	NOUN
bracis-33554	101	41	\infty	\infty	PROPN
bracis-33554	101	42	}	}	PUNCT
bracis-33554	101	43	e\left	e\left	VERB
bracis-33554	101	44	[	[	PUNCT
bracis-33554	101	45	\sum	\sum	NOUN
bracis-33554	101	46	_	_	PUNCT
bracis-33554	101	47	{	{	PUNCT
bracis-33554	101	48	n=1}^{n+1	n=1}^{n+1	ADJ
bracis-33554	101	49	}	}	PUNCT
bracis-33554	101	50	r_{n	r_{n	PROPN
bracis-33554	101	51	}	}	PUNCT
bracis-33554	101	52	\sum	\sum	NOUN
bracis-33554	101	53	_	_	PUNCT
bracis-33554	101	54	{	{	PUNCT
bracis-33554	101	55	n=1}^{n	n=1}^{n	ADJ
bracis-33554	101	56	}	}	PUNCT
bracis-33554	101	57	r_{n	r_{n	PROPN
bracis-33554	101	58	}	}	PUNCT
bracis-33554	101	59	\right	\right	PROPN
bracis-33554	101	60	]	]	PUNCT
bracis-33554	101	61	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	101	62	(	(	PUNCT
bracis-33554	101	63	16	16	NUM
bracis-33554	101	64	)	)	PUNCT
bracis-33554	101	65	$	$	SYM
bracis-33554	101	66	$	$	SYM
bracis-33554	101	67	\begin{aligned	\begin{aligne	VERB
bracis-33554	101	68	}	}	PUNCT
bracis-33554	101	69	&	&	CCONJ
bracis-33554	101	70	=	=	SYM
bracis-33554	101	71	\lim	\lim	PROPN
bracis-33554	101	72	_	_	PUNCT
bracis-33554	101	73	{	{	PUNCT
bracis-33554	101	74	n\rightarrow	n\rightarrow	NOUN
bracis-33554	101	75	\infty	\infty	VERB
bracis-33554	101	76	}	}	PUNCT
bracis-33554	101	77	\sum	\sum	NOUN
bracis-33554	101	78	_	_	PUNCT
bracis-33554	101	79	{	{	PUNCT
bracis-33554	101	80	n=1}^{n	n=1}^{n	ADJ
bracis-33554	101	81	}	}	PUNCT
bracis-33554	101	82	\frac{1}{n	\frac{1}{n	NOUN
bracis-33554	101	83	}	}	PUNCT
bracis-33554	101	84	e[r_{n	e[r_{n	ADP
bracis-33554	101	85	}	}	PUNCT
bracis-33554	101	86	]	]	PUNCT
bracis-33554	101	87	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	101	88	(	(	PUNCT
bracis-33554	101	89	17	17	NUM
bracis-33554	101	90	)	)	PUNCT
bracis-33554	101	91	$	$	SYM
bracis-33554	101	92	$	$	SYM
bracis-33554	101	93	\begin{aligned	\begin{aligne	VERB
bracis-33554	101	94	}	}	PUNCT
bracis-33554	101	95	&	&	CCONJ
bracis-33554	101	96	=	=	SYM
bracis-33554	101	97	\lim	\lim	PROPN
bracis-33554	101	98	_	_	PUNCT
bracis-33554	101	99	{	{	PUNCT
bracis-33554	101	100	n\rightarrow	n\rightarrow	NOUN
bracis-33554	101	101	\infty	\infty	VERB
bracis-33554	101	102	}	}	PUNCT
bracis-33554	102	1	\sum	\sum	NOUN
bracis-33554	102	2	_	_	PUNCT
bracis-33554	102	3	{	{	PUNCT
bracis-33554	102	4	n=1}^{n	n=1}^{n	ADV
bracis-33554	102	5	}	}	PUNCT
bracis-33554	102	6	\frac{1}{nh	\frac{1}{nh	ADJ
bracis-33554	102	7	}	}	PUNCT
bracis-33554	102	8	e\left	e\left	VERB
bracis-33554	102	9	[	[	PUNCT
bracis-33554	102	10	\sum	\sum	NOUN
bracis-33554	102	11	_	_	PUNCT
bracis-33554	102	12	{	{	PUNCT
bracis-33554	102	13	i	i	PROPN
bracis-33554	102	14	=	=	SYM
bracis-33554	102	15	n}^{n+h	n}^{n+h	PROPN
bracis-33554	102	16	}	}	PUNCT
bracis-33554	102	17	r_{i}\right	r_{i}\right	VERB
bracis-33554	102	18	]	]	PUNCT
bracis-33554	102	19	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	102	20	(	(	PUNCT
bracis-33554	102	21	18	18	NUM
bracis-33554	102	22	)	)	PUNCT
bracis-33554	102	23	equation	equation	NOUN
bracis-33554	102	24	 	 	SPACE
bracis-33554	102	25	15	15	NUM
bracis-33554	102	26	was	be	AUX
bracis-33554	102	27	described	describe	VERB
bracis-33554	102	28	before	before	ADV
bracis-33554	102	29	.	.	PUNCT
bracis-33554	103	1	equation	equation	NOUN
bracis-33554	103	2	 	 	SPACE
bracis-33554	103	3	16	16	NUM
bracis-33554	103	4	interprets	interpret	VERB
bracis-33554	103	5	gain	gain	NOUN
bracis-33554	103	6	as	as	ADP
bracis-33554	103	7	the	the	DET
bracis-33554	103	8	increase	increase	NOUN
bracis-33554	103	9	in	in	ADP
bracis-33554	103	10	reward	reward	NOUN
bracis-33554	103	11	at	at	ADP
bracis-33554	103	12	each	each	DET
bracis-33554	103	13	decision	decision	NOUN
bracis-33554	103	14	step	step	NOUN
bracis-33554	103	15	.	.	PUNCT
bracis-33554	104	1	in	in	ADP
bracis-33554	104	2	this	this	DET
bracis-33554	104	3	approach	approach	NOUN
bracis-33554	104	4	,	,	PUNCT
bracis-33554	104	5	the	the	DET
bracis-33554	104	6	value	value	NOUN
bracis-33554	104	7	is	be	AUX
bracis-33554	104	8	calculated	calculate	VERB
bracis-33554	104	9	as	as	ADP
bracis-33554	104	10	the	the	DET
bracis-33554	104	11	difference	difference	NOUN
bracis-33554	104	12	between	between	ADP
bracis-33554	104	13	the	the	DET
bracis-33554	104	14	expected	expect	VERB
bracis-33554	104	15	accumulated	accumulate	VERB
bracis-33554	104	16	rewards	reward	NOUN
bracis-33554	104	17	considering	consider	VERB
bracis-33554	104	18	two	two	NUM
bracis-33554	104	19	consecutive	consecutive	ADJ
bracis-33554	104	20	time	time	NOUN
bracis-33554	104	21	steps	step	NOUN
bracis-33554	104	22	.	.	PUNCT
bracis-33554	105	1	even	even	ADV
bracis-33554	105	2	though	though	SCONJ
bracis-33554	105	3	each	each	DET
bracis-33554	105	4	accumulated	accumulate	VERB
bracis-33554	105	5	reward	reward	NOUN
bracis-33554	105	6	tends	tend	VERB
bracis-33554	105	7	to	to	PART
bracis-33554	105	8	infinity	infinity	VERB
bracis-33554	105	9	,	,	PUNCT
bracis-33554	105	10	the	the	DET
bracis-33554	105	11	difference	difference	NOUN
bracis-33554	105	12	between	between	ADP
bracis-33554	105	13	them	they	PRON
bracis-33554	105	14	is	be	AUX
bracis-33554	105	15	finite	finite	ADJ
bracis-33554	105	16	.	.	PUNCT
bracis-33554	106	1	this	this	DET
bracis-33554	106	2	approach	approach	NOUN
bracis-33554	106	3	is	be	AUX
bracis-33554	106	4	similar	similar	ADJ
bracis-33554	106	5	to	to	ADP
bracis-33554	106	6	the	the	DET
bracis-33554	106	7	gain	gain	NOUN
bracis-33554	106	8	extracted	extract	VERB
bracis-33554	106	9	in	in	ADP
bracis-33554	106	10	iterative	iterative	ADJ
bracis-33554	106	11	algorithms	algorithm	NOUN
bracis-33554	106	12	,	,	PUNCT
bracis-33554	106	13	such	such	ADJ
bracis-33554	106	14	as	as	ADP
bracis-33554	106	15	the	the	DET
bracis-33554	106	16	relative	relative	ADJ
bracis-33554	106	17	value	value	NOUN
bracis-33554	106	18	iteration	iteration	NOUN
bracis-33554	106	19	algorithm	algorithm	NOUN
bracis-33554	106	20	[	[	X
bracis-33554	106	21	4	4	NUM
bracis-33554	106	22	]	]	PUNCT
bracis-33554	106	23	.	.	PUNCT
bracis-33554	107	1	equation	equation	NOUN
bracis-33554	107	2	 	 	SPACE
bracis-33554	107	3	17	17	NUM
bracis-33554	107	4	considers	consider	VERB
bracis-33554	107	5	the	the	DET
bracis-33554	107	6	immediate	immediate	ADJ
bracis-33554	107	7	reward	reward	NOUN
bracis-33554	107	8	as	as	ADP
bracis-33554	107	9	a	a	DET
bracis-33554	107	10	random	random	ADJ
bracis-33554	107	11	variable	variable	NOUN
bracis-33554	107	12	.	.	PUNCT
bracis-33554	108	1	the	the	DET
bracis-33554	108	2	gain	gain	NOUN
bracis-33554	108	3	is	be	AUX
bracis-33554	108	4	interpreted	interpret	VERB
bracis-33554	108	5	as	as	ADP
bracis-33554	108	6	the	the	DET
bracis-33554	108	7	sum	sum	NOUN
bracis-33554	108	8	of	of	ADP
bracis-33554	108	9	the	the	DET
bracis-33554	108	10	expected	expect	VERB
bracis-33554	108	11	immediate	immediate	ADJ
bracis-33554	108	12	rewards	reward	NOUN
bracis-33554	108	13	divided	divide	VERB
bracis-33554	108	14	by	by	ADP
bracis-33554	108	15	n.	n.	NOUN
bracis-33554	108	16	equation	equation	NOUN
bracis-33554	108	17	 	 	SPACE
bracis-33554	108	18	18	18	NUM
bracis-33554	108	19	conjectures	conjecture	VERB
bracis-33554	108	20	the	the	DET
bracis-33554	108	21	interpretation	interpretation	NOUN
bracis-33554	108	22	of	of	ADP
bracis-33554	108	23	the	the	DET
bracis-33554	108	24	gain	gain	NOUN
bracis-33554	108	25	as	as	ADP
bracis-33554	108	26	the	the	DET
bracis-33554	108	27	cesaro	cesaro	NOUN
bracis-33554	108	28	limit	limit	NOUN
bracis-33554	108	29	of	of	ADP
bracis-33554	108	30	the	the	DET
bracis-33554	108	31	expected	expect	VERB
bracis-33554	108	32	accumulated	accumulate	VERB
bracis-33554	108	33	reward	reward	NOUN
bracis-33554	108	34	for	for	ADP
bracis-33554	108	35	h	h	NOUN
bracis-33554	108	36	decision	decision	NOUN
bracis-33554	108	37	steps	step	NOUN
bracis-33554	108	38	after	after	ADP
bracis-33554	108	39	time	time	NOUN
bracis-33554	108	40	n.	n.	PROPN
bracis-33554	108	41	in	in	ADP
bracis-33554	108	42	this	this	DET
bracis-33554	108	43	equation	equation	NOUN
bracis-33554	108	44	,	,	PUNCT
bracis-33554	108	45	the	the	DET
bracis-33554	108	46	random	random	ADJ
bracis-33554	108	47	variable	variable	NOUN
bracis-33554	108	48	is	be	AUX
bracis-33554	108	49	the	the	DET
bracis-33554	108	50	accumulated	accumulate	VERB
bracis-33554	108	51	reward	reward	NOUN
bracis-33554	108	52	of	of	ADP
bracis-33554	108	53	trajectories	trajectory	NOUN
bracis-33554	108	54	of	of	ADP
bracis-33554	108	55	fixed	fix	VERB
bracis-33554	108	56	size	size	NOUN
bracis-33554	108	57	h.	h.	PROPN
bracis-33554	108	58	the	the	DET
bracis-33554	108	59	division	division	NOUN
bracis-33554	108	60	is	be	AUX
bracis-33554	108	61	done	do	VERB
bracis-33554	108	62	by	by	ADP
bracis-33554	108	63	nh	nh	PROPN
bracis-33554	108	64	because	because	SCONJ
bracis-33554	108	65	n	n	NUM
bracis-33554	108	66	sums	sum	NOUN
bracis-33554	108	67	of	of	ADP
bracis-33554	108	68	h	h	NOUN
bracis-33554	108	69	rewards	reward	NOUN
bracis-33554	108	70	are	be	AUX
bracis-33554	108	71	made	make	VERB
bracis-33554	108	72	.	.	PUNCT
bracis-33554	109	1	note	note	VERB
bracis-33554	109	2	that	that	SCONJ
bracis-33554	109	3	eqs	eqs	PROPN
bracis-33554	109	4	.	.	PUNCT
bracis-33554	109	5	 	 	SPACE
bracis-33554	109	6	16	16	NUM
bracis-33554	109	7	,	,	PUNCT
bracis-33554	109	8	17	17	NUM
bracis-33554	109	9	and	and	CCONJ
bracis-33554	109	10	18	18	NUM
bracis-33554	109	11	converge	converge	NOUN
bracis-33554	109	12	to	to	ADP
bracis-33554	109	13	some	some	DET
bracis-33554	109	14	distribution	distribution	NOUN
bracis-33554	109	15	,	,	PUNCT
bracis-33554	109	16	allowing	allow	VERB
bracis-33554	109	17	the	the	DET
bracis-33554	109	18	use	use	NOUN
bracis-33554	109	19	of	of	ADP
bracis-33554	109	20	the	the	DET
bracis-33554	109	21	steady	steady	ADJ
bracis-33554	109	22	-	-	PUNCT
bracis-33554	109	23	state	state	NOUN
bracis-33554	109	24	matrix	matrix	NOUN
bracis-33554	109	25	\(p^*_\pi	\(p^*_\pi	NOUN
bracis-33554	109	26	\	\	NOUN
bracis-33554	109	27	)	)	PUNCT
bracis-33554	109	28	to	to	PART
bracis-33554	109	29	calculate	calculate	VERB
bracis-33554	109	30	the	the	DET
bracis-33554	109	31	gain	gain	NOUN
bracis-33554	109	32	.	.	PUNCT
bracis-33554	110	1	3.2	3.2	NUM
bracis-33554	110	2	formalization	formalization	NOUN
bracis-33554	110	3	of	of	ADP
bracis-33554	110	4	the	the	DET
bracis-33554	110	5	risk	risk	NOUN
bracis-33554	110	6	-	-	PUNCT
bracis-33554	110	7	sensitive	sensitive	ADJ
bracis-33554	110	8	criterion	criterion	NOUN
bracis-33554	110	9	before	before	ADP
bracis-33554	110	10	formalizing	formalize	VERB
bracis-33554	110	11	the	the	DET
bracis-33554	110	12	risk	risk	NOUN
bracis-33554	110	13	-	-	PUNCT
bracis-33554	110	14	sensitive	sensitive	ADJ
bracis-33554	110	15	criterion	criterion	NOUN
bracis-33554	110	16	,	,	PUNCT
bracis-33554	110	17	some	some	DET
bracis-33554	110	18	notations	notation	NOUN
bracis-33554	110	19	used	use	VERB
bracis-33554	110	20	in	in	ADP
bracis-33554	110	21	this	this	DET
bracis-33554	110	22	section	section	NOUN
bracis-33554	110	23	are	be	AUX
bracis-33554	110	24	introduced	introduce	VERB
bracis-33554	110	25	.	.	PUNCT
bracis-33554	111	1	let	let	AUX
bracis-33554	111	2	\(\psi	\(\psi	VERB
bracis-33554	111	3	\	\	NOUN
bracis-33554	111	4	)	)	PUNCT
bracis-33554	111	5	be	be	AUX
bracis-33554	111	6	a	a	DET
bracis-33554	111	7	sequence	sequence	NOUN
bracis-33554	111	8	of	of	ADP
bracis-33554	111	9	states	state	NOUN
bracis-33554	111	10	and	and	CCONJ
bracis-33554	111	11	\(\psi	\(\psi	NOUN
bracis-33554	111	12	(	(	PUNCT
bracis-33554	111	13	k)\	k)\	NOUN
bracis-33554	111	14	)	)	PUNCT
bracis-33554	111	15	be	be	VERB
bracis-33554	111	16	the	the	DET
bracis-33554	111	17	k	k	PROPN
bracis-33554	111	18	-	-	PUNCT
bracis-33554	111	19	th	th	VERB
bracis-33554	111	20	state	state	NOUN
bracis-33554	111	21	of	of	ADP
bracis-33554	111	22	this	this	DET
bracis-33554	111	23	sequence	sequence	NOUN
bracis-33554	111	24	.	.	PUNCT
bracis-33554	112	1	let	let	VERB
bracis-33554	112	2	\(s^h\	\(s^h\	NUM
bracis-33554	112	3	)	)	PUNCT
bracis-33554	112	4	be	be	VERB
bracis-33554	112	5	the	the	DET
bracis-33554	112	6	set	set	NOUN
bracis-33554	112	7	of	of	ADP
bracis-33554	112	8	all	all	DET
bracis-33554	112	9	sequences	sequence	NOUN
bracis-33554	112	10	\(\psi	\(\psi	VERB
bracis-33554	112	11	\	\	NOUN
bracis-33554	112	12	)	)	PUNCT
bracis-33554	112	13	of	of	ADP
bracis-33554	112	14	size	size	NOUN
bracis-33554	112	15	h.	h.	PROPN
bracis-33554	112	16	let	let	VERB
bracis-33554	112	17	\(f_{s	\(f_{s	NOUN
bracis-33554	112	18	,	,	PUNCT
bracis-33554	112	19	n}^{\pi	n}^{\pi	PROPN
bracis-33554	112	20	,	,	PUNCT
bracis-33554	112	21	h	h	NOUN
bracis-33554	112	22	}	}	PUNCT
bracis-33554	112	23	:	:	PUNCT
bracis-33554	113	1	s^h	s^h	VERB
bracis-33554	113	2	\rightarrow	\rightarrow	PROPN
bracis-33554	113	3	[	[	X
bracis-33554	113	4	0,1]\	0,1]\	NOUN
bracis-33554	113	5	)	)	PUNCT
bracis-33554	113	6	,	,	PUNCT
bracis-33554	113	7	\(f_{s	\(f_{s	NOUN
bracis-33554	113	8	,	,	PUNCT
bracis-33554	113	9	n}^{\pi	n}^{\pi	PROPN
bracis-33554	113	10	,	,	PUNCT
bracis-33554	113	11	h}(\psi	h}(\psi	NUM
bracis-33554	113	12	)	)	PUNCT
bracis-33554	113	13	\	\	NOUN
bracis-33554	113	14	)	)	PUNCT
bracis-33554	113	15	is	be	AUX
bracis-33554	113	16	the	the	DET
bracis-33554	113	17	probability	probability	NOUN
bracis-33554	113	18	of	of	ADP
bracis-33554	113	19	the	the	DET
bracis-33554	113	20	sequence	sequence	NOUN
bracis-33554	113	21	\(\psi	\(\psi	VERB
bracis-33554	113	22	\	\	NOUN
bracis-33554	113	23	)	)	PUNCT
bracis-33554	113	24	of	of	ADP
bracis-33554	113	25	size	size	NOUN
bracis-33554	113	26	h	h	NOUN
bracis-33554	113	27	occurring	occur	VERB
bracis-33554	113	28	with	with	ADP
bracis-33554	113	29	the	the	DET
bracis-33554	113	30	process	process	NOUN
bracis-33554	113	31	being	be	AUX
bracis-33554	113	32	started	start	VERB
bracis-33554	113	33	in	in	ADP
bracis-33554	113	34	state	state	NOUN
bracis-33554	113	35	s	s	NOUN
bracis-33554	113	36	and	and	CCONJ
bracis-33554	113	37	time	time	NOUN
bracis-33554	113	38	n	n	CCONJ
bracis-33554	113	39	,	,	PUNCT
bracis-33554	113	40	and	and	CCONJ
bracis-33554	113	41	can	can	AUX
bracis-33554	113	42	be	be	AUX
bracis-33554	113	43	calculated	calculate	VERB
bracis-33554	113	44	 	 	SPACE
bracis-33554	113	45	as	as	ADP
bracis-33554	113	46	$	$	SYM
bracis-33554	113	47	$	$	SYM
bracis-33554	113	48	\begin{aligned	\begin{aligne	VERB
bracis-33554	113	49	}	}	PUNCT
bracis-33554	113	50	\begin{aligned	\begin{aligne	VERB
bracis-33554	113	51	}	}	PUNCT
bracis-33554	113	52	f_{s	f_{s	PROPN
bracis-33554	113	53	,	,	PUNCT
bracis-33554	113	54	n}^{\pi	n}^{\pi	PROPN
bracis-33554	113	55	,	,	PUNCT
bracis-33554	113	56	h}(\psi	h}(\psi	NUM
bracis-33554	113	57	)	)	PUNCT
bracis-33554	113	58	&	&	CCONJ
bracis-33554	113	59	=	=	PROPN
bracis-33554	113	60	pr\left	pr\left	PROPN
bracis-33554	113	61	(	(	PUNCT
bracis-33554	113	62	\bigwedge	\bigwedge	NOUN
bracis-33554	113	63	_	_	PROPN
bracis-33554	113	64	{	{	PUNCT
bracis-33554	113	65	k=0}^{h-1	k=0}^{h-1	NOUN
bracis-33554	113	66	}	}	PUNCT
bracis-33554	113	67	s_{n+k}=\psi	s_{n+k}=\psi	NOUN
bracis-33554	113	68	(	(	PUNCT
bracis-33554	113	69	k	k	NOUN
bracis-33554	113	70	)	)	PUNCT
bracis-33554	113	71	|	|	ADV
bracis-33554	113	72	s_{0}=s\right	s_{0}=s\right	NOUN
bracis-33554	113	73	)	)	PUNCT
bracis-33554	113	74	\\	\\	NOUN
bracis-33554	113	75	&	&	CCONJ
bracis-33554	113	76	=	=	PUNCT
bracis-33554	113	77	pr\left	pr\left	PROPN
bracis-33554	113	78	(	(	PUNCT
bracis-33554	113	79	s_{n+0}=\psi	s_{n+0}=\psi	PROPN
bracis-33554	113	80	(	(	PUNCT
bracis-33554	113	81	0	0	NUM
bracis-33554	113	82	)	)	PUNCT
bracis-33554	113	83	|	|	ADV
bracis-33554	113	84	s_{0}=s)\prod	s_{0}=s)\prod	X
bracis-33554	114	1	_	_	NOUN
bracis-33554	114	2	{	{	PUNCT
bracis-33554	114	3	k=1}^{h-1}pr(s_{n+k}=\psi	k=1}^{h-1}pr(s_{n+k}=\psi	PROPN
bracis-33554	114	4	(	(	PUNCT
bracis-33554	114	5	k)|s_{n+k-1}=\psi	k)|s_{n+k-1}=\psi	PROPN
bracis-33554	114	6	(	(	PUNCT
bracis-33554	114	7	k-1)\right	k-1)\right	PROPN
bracis-33554	114	8	)	)	PUNCT
bracis-33554	114	9	.	.	PUNCT
bracis-33554	115	1	\end{aligned	\end{aligne	VERB
bracis-33554	115	2	}	}	PUNCT
bracis-33554	115	3	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	115	4	(	(	PUNCT
bracis-33554	115	5	19	19	NUM
bracis-33554	115	6	)	)	PUNCT
bracis-33554	115	7	let	let	VERB
bracis-33554	115	8	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	115	9	,	,	PUNCT
bracis-33554	115	10	h}_n(\psi	h}_n(\psi	VERB
bracis-33554	115	11	)	)	PUNCT
bracis-33554	115	12	\	\	NOUN
bracis-33554	115	13	)	)	PUNCT
bracis-33554	115	14	be	be	AUX
bracis-33554	115	15	the	the	DET
bracis-33554	115	16	accumulated	accumulate	VERB
bracis-33554	115	17	reward	reward	NOUN
bracis-33554	115	18	of	of	ADP
bracis-33554	115	19	the	the	DET
bracis-33554	115	20	sequence	sequence	NOUN
bracis-33554	115	21	\(\psi	\(\psi	VERB
bracis-33554	115	22	\	\	NOUN
bracis-33554	115	23	)	)	PUNCT
bracis-33554	115	24	of	of	ADP
bracis-33554	115	25	size	size	NOUN
bracis-33554	115	26	h	h	NOUN
bracis-33554	115	27	with	with	ADP
bracis-33554	115	28	the	the	DET
bracis-33554	115	29	process	process	NOUN
bracis-33554	115	30	starting	start	VERB
bracis-33554	115	31	at	at	ADP
bracis-33554	115	32	time	time	NOUN
bracis-33554	115	33	n	n	CCONJ
bracis-33554	116	1	$	$	SYM
bracis-33554	116	2	$	$	SYM
bracis-33554	116	3	\begin{aligned	\begin{aligne	VERB
bracis-33554	116	4	}	}	PUNCT
bracis-33554	116	5	v^{\pi	v^{\pi	NOUN
bracis-33554	116	6	,	,	PUNCT
bracis-33554	116	7	h}_n(\psi	h}_n(\psi	VERB
bracis-33554	116	8	)	)	PUNCT
bracis-33554	117	1	=	=	SYM
bracis-33554	117	2	\sum	\sum	NOUN
bracis-33554	117	3	_	_	PUNCT
bracis-33554	117	4	{	{	PUNCT
bracis-33554	117	5	k	k	X
bracis-33554	117	6	=	=	ADJ
bracis-33554	117	7	n}^{n+h-1	n}^{n+h-1	ADJ
bracis-33554	117	8	}	}	PUNCT
bracis-33554	117	9	r	r	NOUN
bracis-33554	117	10	(	(	PUNCT
bracis-33554	117	11	\psi	\psi	PROPN
bracis-33554	117	12	(	(	PUNCT
bracis-33554	117	13	k	k	NOUN
bracis-33554	117	14	)	)	PUNCT
bracis-33554	117	15	)	)	PUNCT
bracis-33554	117	16	.	.	PUNCT
bracis-33554	118	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	118	2	(	(	PUNCT
bracis-33554	118	3	20	20	NUM
bracis-33554	118	4	)	)	PUNCT
bracis-33554	118	5	risk	risk	NOUN
bracis-33554	118	6	-	-	PUNCT
bracis-33554	118	7	sensitive	sensitive	ADJ
bracis-33554	118	8	criterion	criterion	NOUN
bracis-33554	118	9	with	with	ADP
bracis-33554	118	10	utility	utility	NOUN
bracis-33554	118	11	function	function	NOUN
bracis-33554	118	12	.	.	PUNCT
bracis-33554	119	1	the	the	DET
bracis-33554	119	2	utility	utility	NOUN
bracis-33554	119	3	function	function	NOUN
bracis-33554	119	4	u	u	NOUN
bracis-33554	119	5	can	can	AUX
bracis-33554	119	6	be	be	AUX
bracis-33554	119	7	applied	apply	VERB
bracis-33554	119	8	either	either	ADV
bracis-33554	119	9	to	to	ADP
bracis-33554	119	10	the	the	DET
bracis-33554	119	11	sum	sum	NOUN
bracis-33554	119	12	of	of	ADP
bracis-33554	119	13	rewards	reward	NOUN
bracis-33554	119	14	or	or	CCONJ
bracis-33554	119	15	directly	directly	ADV
bracis-33554	119	16	to	to	ADP
bracis-33554	119	17	the	the	DET
bracis-33554	119	18	immediate	immediate	ADJ
bracis-33554	119	19	reward	reward	NOUN
bracis-33554	119	20	.	.	PUNCT
bracis-33554	120	1	the	the	DET
bracis-33554	120	2	average	average	NOUN
bracis-33554	120	3	of	of	ADP
bracis-33554	120	4	the	the	DET
bracis-33554	120	5	expected	expect	VERB
bracis-33554	120	6	utility	utility	NOUN
bracis-33554	120	7	of	of	ADP
bracis-33554	120	8	the	the	DET
bracis-33554	120	9	accumulated	accumulate	VERB
bracis-33554	120	10	reward	reward	NOUN
bracis-33554	120	11	is	be	AUX
bracis-33554	120	12	observed	observe	VERB
bracis-33554	120	13	in	in	ADP
bracis-33554	120	14	eq	eq	PROPN
bracis-33554	120	15	.	.	PUNCT
bracis-33554	120	16	 	 	SPACE
bracis-33554	120	17	21	21	NUM
bracis-33554	120	18	and	and	CCONJ
bracis-33554	120	19	represents	represent	VERB
bracis-33554	120	20	the	the	DET
bracis-33554	120	21	approach	approach	NOUN
bracis-33554	120	22	of	of	ADP
bracis-33554	120	23	howard	howard	PROPN
bracis-33554	120	24	and	and	CCONJ
bracis-33554	120	25	matheson	matheson	PROPN
bracis-33554	121	1	[	[	X
bracis-33554	121	2	2	2	NUM
bracis-33554	121	3	]	]	PUNCT
bracis-33554	121	4	,	,	PUNCT
bracis-33554	121	5	which	which	PRON
bracis-33554	121	6	uses	use	VERB
bracis-33554	121	7	the	the	DET
bracis-33554	121	8	exponential	exponential	ADJ
bracis-33554	121	9	utility	utility	NOUN
bracis-33554	121	10	function	function	NOUN
bracis-33554	121	11	.	.	PUNCT
bracis-33554	122	1	this	this	DET
bracis-33554	122	2	equation	equation	NOUN
bracis-33554	122	3	is	be	AUX
bracis-33554	122	4	similar	similar	ADJ
bracis-33554	122	5	to	to	ADP
bracis-33554	122	6	eq	eq	PROPN
bracis-33554	122	7	.	.	PUNCT
bracis-33554	122	8	 	 	SPACE
bracis-33554	122	9	15	15	NUM
bracis-33554	122	10	,	,	PUNCT
bracis-33554	122	11	but	but	CCONJ
bracis-33554	122	12	it	it	PRON
bracis-33554	122	13	includes	include	VERB
bracis-33554	122	14	applying	apply	VERB
bracis-33554	122	15	the	the	DET
bracis-33554	122	16	utility	utility	NOUN
bracis-33554	122	17	function	function	NOUN
bracis-33554	122	18	u	u	NOUN
bracis-33554	122	19	to	to	ADP
bracis-33554	122	20	the	the	DET
bracis-33554	122	21	sum	sum	NOUN
bracis-33554	122	22	of	of	ADP
bracis-33554	122	23	rewards	reward	NOUN
bracis-33554	122	24	$	$	SYM
bracis-33554	122	25	$	$	SYM
bracis-33554	122	26	\begin{aligned	\begin{aligne	VERB
bracis-33554	122	27	}	}	PUNCT
bracis-33554	122	28	g^\pi	g^\pi	VERB
bracis-33554	122	29	_	_	PRON
bracis-33554	122	30	{	{	PUNCT
bracis-33554	122	31	u	u	NOUN
bracis-33554	122	32	}	}	PUNCT
bracis-33554	122	33	=	=	PUNCT
bracis-33554	122	34	\lim	\lim	NOUN
bracis-33554	122	35	_	_	PUNCT
bracis-33554	122	36	{	{	PUNCT
bracis-33554	122	37	n\rightarrow	n\rightarrow	NOUN
bracis-33554	122	38	\infty	\infty	PROPN
bracis-33554	122	39	}	}	PUNCT
bracis-33554	122	40	\frac{1}{n	\frac{1}{n	NOUN
bracis-33554	122	41	}	}	PUNCT
bracis-33554	122	42	e\left	e\left	VERB
bracis-33554	122	43	[	[	PUNCT
bracis-33554	122	44	u\left	u\left	NOUN
bracis-33554	122	45	(	(	PUNCT
bracis-33554	122	46	\sum	\sum	NOUN
bracis-33554	122	47	_	_	PUNCT
bracis-33554	122	48	{	{	PUNCT
bracis-33554	122	49	n=1}^{n	n=1}^{n	ADJ
bracis-33554	122	50	}	}	PUNCT
bracis-33554	122	51	r_{n	r_{n	PROPN
bracis-33554	122	52	}	}	PUNCT
bracis-33554	122	53	\right	\right	PROPN
bracis-33554	122	54	)	)	PUNCT
bracis-33554	122	55	\right	\right	NOUN
bracis-33554	122	56	]	]	PUNCT
bracis-33554	122	57	.	.	PUNCT
bracis-33554	123	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	123	2	(	(	PUNCT
bracis-33554	123	3	21	21	NUM
bracis-33554	123	4	)	)	PUNCT
bracis-33554	123	5	equation	equation	NOUN
bracis-33554	123	6	 	 	SPACE
bracis-33554	123	7	22	22	NUM
bracis-33554	123	8	is	be	AUX
bracis-33554	123	9	equivalent	equivalent	ADJ
bracis-33554	123	10	to	to	ADP
bracis-33554	123	11	eq	eq	PROPN
bracis-33554	123	12	.	.	PUNCT
bracis-33554	123	13	 	 	SPACE
bracis-33554	124	1	21	21	NUM
bracis-33554	124	2	.	.	PUNCT
bracis-33554	125	1	it	it	PRON
bracis-33554	125	2	calculates	calculate	VERB
bracis-33554	125	3	the	the	DET
bracis-33554	125	4	expected	expect	VERB
bracis-33554	125	5	value	value	NOUN
bracis-33554	125	6	of	of	ADP
bracis-33554	125	7	the	the	DET
bracis-33554	125	8	utility	utility	NOUN
bracis-33554	125	9	of	of	ADP
bracis-33554	125	10	the	the	DET
bracis-33554	125	11	accumulated	accumulate	VERB
bracis-33554	125	12	reward	reward	NOUN
bracis-33554	125	13	of	of	ADP
bracis-33554	125	14	all	all	DET
bracis-33554	125	15	sequences	sequence	NOUN
bracis-33554	125	16	of	of	ADP
bracis-33554	125	17	size	size	NOUN
bracis-33554	125	18	\(n\rightarrow	\(n\rightarrow	NOUN
bracis-33554	125	19	\infty	\infty	PROPN
bracis-33554	125	20	\	\	PROPN
bracis-33554	125	21	)	)	PUNCT
bracis-33554	125	22	that	that	PRON
bracis-33554	125	23	start	start	VERB
bracis-33554	125	24	in	in	ADP
bracis-33554	125	25	state	state	NOUN
bracis-33554	125	26	s	s	NOUN
bracis-33554	125	27	and	and	CCONJ
bracis-33554	125	28	at	at	ADP
bracis-33554	125	29	time	time	NOUN
bracis-33554	125	30	1	1	NUM
bracis-33554	125	31	.	.	PUNCT
bracis-33554	126	1	then	then	ADV
bracis-33554	126	2	the	the	DET
bracis-33554	126	3	average	average	NOUN
bracis-33554	126	4	of	of	ADP
bracis-33554	126	5	this	this	DET
bracis-33554	126	6	expected	expect	VERB
bracis-33554	126	7	value	value	NOUN
bracis-33554	126	8	is	be	AUX
bracis-33554	126	9	calculated	calculate	VERB
bracis-33554	126	10	 	 	SPACE
bracis-33554	126	11	by	by	ADP
bracis-33554	126	12	$	$	SYM
bracis-33554	126	13	$	$	SYM
bracis-33554	126	14	\begin{aligned	\begin{aligne	VERB
bracis-33554	126	15	}	}	PUNCT
bracis-33554	126	16	\begin{aligned	\begin{aligne	VERB
bracis-33554	126	17	}	}	PUNCT
bracis-33554	126	18	g^\pi	g^\pi	VERB
bracis-33554	126	19	_	_	PROPN
bracis-33554	126	20	u	u	NOUN
bracis-33554	126	21	&	&	CCONJ
bracis-33554	126	22	=	=	NOUN
bracis-33554	126	23	\lim	\lim	NOUN
bracis-33554	126	24	_	_	PUNCT
bracis-33554	126	25	{	{	PUNCT
bracis-33554	126	26	n\rightarrow	n\rightarrow	NOUN
bracis-33554	126	27	\infty	\infty	VERB
bracis-33554	126	28	}	}	PUNCT
bracis-33554	126	29	\frac{1	\frac{1	ADV
bracis-33554	126	30	}	}	PUNCT
bracis-33554	126	31	{	{	PUNCT
bracis-33554	126	32	n	n	CCONJ
bracis-33554	126	33	}	}	PUNCT
bracis-33554	127	1	\sum	\sum	NOUN
bracis-33554	127	2	_	_	NOUN
bracis-33554	127	3	{	{	PUNCT
bracis-33554	127	4	\psi	\psi	PROPN
bracis-33554	127	5	\in	\in	PROPN
bracis-33554	127	6	{	{	PUNCT
bracis-33554	127	7	s^{n	s^{n	NUM
bracis-33554	127	8	}	}	PUNCT
bracis-33554	127	9	}	}	PUNCT
bracis-33554	127	10	}	}	PUNCT
bracis-33554	127	11	f_{s,1}^{\pi	f_{s,1}^{\pi	VERB
bracis-33554	127	12	,	,	PUNCT
bracis-33554	127	13	n}(\psi	n}(\psi	NUM
bracis-33554	127	14	)	)	PUNCT
bracis-33554	127	15	u\left	u\left	PROPN
bracis-33554	127	16	(	(	PUNCT
bracis-33554	127	17	\sum	\sum	NOUN
bracis-33554	127	18	_	_	PUNCT
bracis-33554	127	19	{	{	PUNCT
bracis-33554	127	20	k=1}^{n	k=1}^{n	NOUN
bracis-33554	127	21	}	}	PUNCT
bracis-33554	127	22	r	r	NOUN
bracis-33554	127	23	(	(	PUNCT
bracis-33554	127	24	\psi	\psi	PROPN
bracis-33554	127	25	(	(	PUNCT
bracis-33554	127	26	k	k	NOUN
bracis-33554	127	27	)	)	PUNCT
bracis-33554	127	28	)	)	PUNCT
bracis-33554	128	1	\right	\right	NOUN
bracis-33554	128	2	)	)	PUNCT
bracis-33554	128	3	.	.	PUNCT
bracis-33554	129	1	\end{aligned	\end{aligne	VERB
bracis-33554	129	2	}	}	PUNCT
bracis-33554	129	3	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	129	4	(	(	PUNCT
bracis-33554	129	5	22	22	NUM
bracis-33554	129	6	)	)	PUNCT
bracis-33554	129	7	when	when	SCONJ
bracis-33554	129	8	\(n\rightarrow	\(n\rightarrow	NOUN
bracis-33554	129	9	\infty	\infty	PROPN
bracis-33554	129	10	\	\	PROPN
bracis-33554	129	11	)	)	PUNCT
bracis-33554	129	12	,	,	PUNCT
bracis-33554	129	13	the	the	DET
bracis-33554	129	14	probability	probability	NOUN
bracis-33554	129	15	of	of	ADP
bracis-33554	129	16	a	a	DET
bracis-33554	129	17	state	state	NOUN
bracis-33554	129	18	occurring	occur	VERB
bracis-33554	129	19	from	from	ADP
bracis-33554	129	20	the	the	DET
bracis-33554	129	21	sequence	sequence	NOUN
bracis-33554	129	22	of	of	ADP
bracis-33554	129	23	states	state	NOUN
bracis-33554	129	24	tends	tend	VERB
bracis-33554	129	25	to	to	ADP
bracis-33554	129	26	the	the	DET
bracis-33554	129	27	steady	steady	ADJ
bracis-33554	129	28	state	state	NOUN
bracis-33554	129	29	at	at	ADP
bracis-33554	129	30	any	any	DET
bracis-33554	129	31	time	time	NOUN
bracis-33554	129	32	\(n\in	\(n\in	PROPN
bracis-33554	129	33	{	{	PUNCT
bracis-33554	129	34	n}\	n}\	NUM
bracis-33554	129	35	)	)	PUNCT
bracis-33554	129	36	,	,	PUNCT
bracis-33554	129	37	so	so	SCONJ
bracis-33554	129	38	that	that	SCONJ
bracis-33554	129	39	the	the	DET
bracis-33554	129	40	probability	probability	NOUN
bracis-33554	129	41	of	of	ADP
bracis-33554	129	42	the	the	DET
bracis-33554	129	43	sequence	sequence	NOUN
bracis-33554	129	44	\(f_{s	\(f_{s	PROPN
bracis-33554	129	45	,	,	PUNCT
bracis-33554	129	46	n}^{\pi	n}^{\pi	PROPN
bracis-33554	129	47	,	,	PUNCT
bracis-33554	129	48	h}\	h}\	PROPN
bracis-33554	129	49	)	)	PUNCT
bracis-33554	129	50	can	can	AUX
bracis-33554	129	51	be	be	AUX
bracis-33554	129	52	calculated	calculate	VERB
bracis-33554	129	53	using	use	VERB
bracis-33554	129	54	the	the	DET
bracis-33554	129	55	steady	steady	ADJ
bracis-33554	129	56	-	-	PUNCT
bracis-33554	129	57	state	state	NOUN
bracis-33554	129	58	probability	probability	NOUN
bracis-33554	129	59	of	of	ADP
bracis-33554	129	60	each	each	DET
bracis-33554	129	61	state	state	NOUN
bracis-33554	129	62	in	in	ADP
bracis-33554	129	63	the	the	DET
bracis-33554	129	64	sequence	sequence	NOUN
bracis-33554	129	65	in	in	ADP
bracis-33554	129	66	eq	eq	PROPN
bracis-33554	129	67	.	.	PUNCT
bracis-33554	129	68	 	 	SPACE
bracis-33554	129	69	19	19	NUM
bracis-33554	129	70	.	.	PUNCT
bracis-33554	130	1	this	this	DET
bracis-33554	130	2	interpretation	interpretation	NOUN
bracis-33554	130	3	introduces	introduce	VERB
bracis-33554	130	4	how	how	SCONJ
bracis-33554	130	5	an	an	DET
bracis-33554	130	6	arbitrary	arbitrary	ADJ
bracis-33554	130	7	sequence	sequence	NOUN
bracis-33554	130	8	of	of	ADP
bracis-33554	130	9	states	state	NOUN
bracis-33554	130	10	is	be	AUX
bracis-33554	130	11	intended	intend	VERB
bracis-33554	130	12	to	to	PART
bracis-33554	130	13	be	be	AUX
bracis-33554	130	14	visualized	visualize	VERB
bracis-33554	130	15	in	in	ADP
bracis-33554	130	16	the	the	DET
bracis-33554	130	17	upcoming	upcoming	ADJ
bracis-33554	130	18	equations	equation	NOUN
bracis-33554	130	19	.	.	PUNCT
bracis-33554	131	1	equation	equation	NOUN
bracis-33554	131	2	 	 	SPACE
bracis-33554	131	3	23	23	NUM
bracis-33554	131	4	calculates	calculate	VERB
bracis-33554	131	5	the	the	DET
bracis-33554	131	6	sum	sum	NOUN
bracis-33554	131	7	of	of	ADP
bracis-33554	131	8	the	the	DET
bracis-33554	131	9	expected	expect	VERB
bracis-33554	131	10	utility	utility	NOUN
bracis-33554	131	11	of	of	ADP
bracis-33554	131	12	the	the	DET
bracis-33554	131	13	accumulated	accumulate	VERB
bracis-33554	131	14	rewards	reward	NOUN
bracis-33554	131	15	of	of	ADP
bracis-33554	131	16	sequences	sequence	NOUN
bracis-33554	131	17	of	of	ADP
bracis-33554	131	18	fixed	fix	VERB
bracis-33554	131	19	size	size	NOUN
bracis-33554	131	20	h	h	NOUN
bracis-33554	131	21	starting	start	VERB
bracis-33554	131	22	at	at	ADP
bracis-33554	131	23	any	any	DET
bracis-33554	131	24	time	time	NOUN
bracis-33554	131	25	n	n	PRON
bracis-33554	131	26	such	such	ADJ
bracis-33554	131	27	that	that	SCONJ
bracis-33554	131	28	\(1\le	\(1\le	PROPN
bracis-33554	131	29	n	n	PRON
bracis-33554	131	30	\le	\le	PROPN
bracis-33554	131	31	{	{	PUNCT
bracis-33554	131	32	n}\	n}\	NUM
bracis-33554	131	33	)	)	PUNCT
bracis-33554	131	34	,	,	PUNCT
bracis-33554	131	35	with	with	ADP
bracis-33554	131	36	\(n\rightarrow	\(n\rightarrow	NOUN
bracis-33554	131	37	\infty	\infty	PROPN
bracis-33554	131	38	\	\	PROPN
bracis-33554	131	39	)	)	PUNCT
bracis-33554	131	40	,	,	PUNCT
bracis-33554	131	41	and	and	CCONJ
bracis-33554	131	42	finally	finally	ADV
bracis-33554	131	43	their	their	PRON
bracis-33554	131	44	average	average	NOUN
bracis-33554	131	45	is	be	AUX
bracis-33554	131	46	calculated	calculate	VERB
bracis-33554	131	47	 	 	SPACE
bracis-33554	131	48	by	by	ADP
bracis-33554	131	49	$	$	SYM
bracis-33554	131	50	$	$	SYM
bracis-33554	131	51	\begin{aligned	\begin{aligne	VERB
bracis-33554	131	52	}	}	PUNCT
bracis-33554	131	53	g_{u}^{\pi	g_{u}^{\pi	NOUN
bracis-33554	131	54	,	,	PUNCT
bracis-33554	131	55	h	h	NOUN
bracis-33554	131	56	}	}	PUNCT
bracis-33554	131	57	=	=	PUNCT
bracis-33554	131	58	\lim	\lim	NOUN
bracis-33554	131	59	_	_	PUNCT
bracis-33554	131	60	{	{	PUNCT
bracis-33554	131	61	n\rightarrow	n\rightarrow	NOUN
bracis-33554	131	62	\infty	\infty	PROPN
bracis-33554	131	63	}	}	PUNCT
bracis-33554	131	64	\frac{1}{n	\frac{1}{n	NOUN
bracis-33554	131	65	}	}	PUNCT
bracis-33554	132	1	\sum	\sum	NOUN
bracis-33554	132	2	_	_	PUNCT
bracis-33554	132	3	{	{	PUNCT
bracis-33554	132	4	n=1}^{n	n=1}^{n	ADV
bracis-33554	132	5	}	}	PUNCT
bracis-33554	132	6	e\left	e\left	VERB
bracis-33554	132	7	[	[	PUNCT
bracis-33554	132	8	u\left	u\left	NOUN
bracis-33554	132	9	(	(	PUNCT
bracis-33554	132	10	\sum	\sum	NOUN
bracis-33554	132	11	_	_	PUNCT
bracis-33554	132	12	{	{	PUNCT
bracis-33554	132	13	i	i	PROPN
bracis-33554	132	14	=	=	NOUN
bracis-33554	132	15	n}^{n+h-1	n}^{n+h-1	ADJ
bracis-33554	132	16	}	}	PUNCT
bracis-33554	132	17	r_{i	r_{i	NOUN
bracis-33554	132	18	}	}	PUNCT
bracis-33554	132	19	\right	\right	NOUN
bracis-33554	132	20	)	)	PUNCT
bracis-33554	132	21	\right	\right	NOUN
bracis-33554	132	22	]	]	PUNCT
bracis-33554	132	23	.	.	PUNCT
bracis-33554	133	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	133	2	(	(	PUNCT
bracis-33554	133	3	23	23	NUM
bracis-33554	133	4	)	)	PUNCT
bracis-33554	133	5	equation	equation	NOUN
bracis-33554	133	6	 	 	SPACE
bracis-33554	133	7	25	25	NUM
bracis-33554	133	8	reinterprets	reinterpret	VERB
bracis-33554	133	9	eq	eq	ADP
bracis-33554	133	10	.	.	PUNCT
bracis-33554	133	11	 	 	SPACE
bracis-33554	133	12	23	23	NUM
bracis-33554	133	13	by	by	ADP
bracis-33554	133	14	inserting	insert	VERB
bracis-33554	133	15	a	a	DET
bracis-33554	133	16	sequence	sequence	NOUN
bracis-33554	133	17	\(\psi	\(\psi	VERB
bracis-33554	133	18	\	\	NOUN
bracis-33554	133	19	)	)	PUNCT
bracis-33554	133	20	of	of	ADP
bracis-33554	133	21	h	h	NOUN
bracis-33554	133	22	states	state	NOUN
bracis-33554	133	23	,	,	PUNCT
bracis-33554	133	24	the	the	DET
bracis-33554	133	25	probability	probability	NOUN
bracis-33554	133	26	of	of	ADP
bracis-33554	133	27	this	this	DET
bracis-33554	133	28	sequence	sequence	NOUN
bracis-33554	133	29	of	of	ADP
bracis-33554	133	30	states	state	NOUN
bracis-33554	133	31	\(f_{s	\(f_{s	ADP
bracis-33554	133	32	,	,	PUNCT
bracis-33554	133	33	n}^	n}^	NOUN
bracis-33554	133	34	{	{	PUNCT
bracis-33554	133	35	\pi	\pi	PROPN
bracis-33554	133	36	,	,	PUNCT
bracis-33554	133	37	h}(\psi	h}(\psi	NUM
bracis-33554	133	38	)	)	PUNCT
bracis-33554	133	39	\	\	NOUN
bracis-33554	133	40	)	)	PUNCT
bracis-33554	133	41	(	(	PUNCT
bracis-33554	133	42	eq	eq	NOUN
bracis-33554	133	43	.	.	PUNCT
bracis-33554	133	44	 	 	SPACE
bracis-33554	133	45	19	19	NUM
bracis-33554	133	46	)	)	PUNCT
bracis-33554	133	47	and	and	CCONJ
bracis-33554	133	48	its	its	PRON
bracis-33554	133	49	accumulated	accumulate	VERB
bracis-33554	133	50	reward	reward	NOUN
bracis-33554	133	51	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	133	52	,	,	PUNCT
bracis-33554	133	53	h}_n(\psi	h}_n(\psi	VERB
bracis-33554	133	54	)	)	PUNCT
bracis-33554	133	55	\	\	PROPN
bracis-33554	133	56	)	)	PUNCT
bracis-33554	133	57	(	(	PUNCT
bracis-33554	133	58	eq	eq	NOUN
bracis-33554	133	59	.	.	PUNCT
bracis-33554	133	60	 	 	SPACE
bracis-33554	133	61	20	20	NUM
bracis-33554	133	62	)	)	PUNCT
bracis-33554	133	63	.	.	PUNCT
bracis-33554	134	1	thus	thus	ADV
bracis-33554	134	2	,	,	PUNCT
bracis-33554	134	3	for	for	ADP
bracis-33554	134	4	each	each	DET
bracis-33554	134	5	sequence	sequence	NOUN
bracis-33554	134	6	of	of	ADP
bracis-33554	134	7	size	size	NOUN
bracis-33554	134	8	h	h	NOUN
bracis-33554	134	9	starting	start	VERB
bracis-33554	134	10	at	at	ADP
bracis-33554	134	11	time	time	NOUN
bracis-33554	134	12	n	n	CCONJ
bracis-33554	134	13	,	,	PUNCT
bracis-33554	134	14	its	its	PRON
bracis-33554	134	15	probability	probability	NOUN
bracis-33554	134	16	is	be	AUX
bracis-33554	134	17	multiplied	multiply	VERB
bracis-33554	134	18	by	by	ADP
bracis-33554	134	19	the	the	DET
bracis-33554	134	20	utility	utility	NOUN
bracis-33554	134	21	of	of	ADP
bracis-33554	134	22	its	its	PRON
bracis-33554	134	23	accumulated	accumulate	VERB
bracis-33554	134	24	reward	reward	NOUN
bracis-33554	134	25	$	$	SYM
bracis-33554	134	26	$	$	SYM
bracis-33554	134	27	\begin{aligned	\begin{aligne	VERB
bracis-33554	134	28	}	}	PUNCT
bracis-33554	134	29	{	{	PUNCT
bracis-33554	134	30	u_{n}^{\pi	u_{n}^{\pi	PROPN
bracis-33554	134	31	,	,	PUNCT
bracis-33554	134	32	h	h	NOUN
bracis-33554	134	33	}	}	PUNCT
bracis-33554	134	34	}	}	PUNCT
bracis-33554	134	35	=	=	SYM
bracis-33554	134	36	\sum	\sum	NOUN
bracis-33554	134	37	_	_	PUNCT
bracis-33554	134	38	{	{	PUNCT
bracis-33554	134	39	\psi	\psi	PROPN
bracis-33554	134	40	\in	\in	PROPN
bracis-33554	134	41	{	{	PUNCT
bracis-33554	134	42	s^h	s^h	NOUN
bracis-33554	134	43	}	}	PUNCT
bracis-33554	134	44	}	}	PUNCT
bracis-33554	134	45	f_{s	f_{s	PROPN
bracis-33554	134	46	,	,	PUNCT
bracis-33554	134	47	n}^{\pi	n}^{\pi	PROPN
bracis-33554	134	48	,	,	PUNCT
bracis-33554	134	49	h}(\psi	h}(\psi	NUM
bracis-33554	134	50	)	)	PUNCT
bracis-33554	134	51	u\left	u\left	PROPN
bracis-33554	134	52	(	(	PUNCT
bracis-33554	134	53	v^{\pi	v^{\pi	PROPN
bracis-33554	134	54	,	,	PUNCT
bracis-33554	134	55	h}_n(\psi	h}_n(\psi	X
bracis-33554	134	56	)	)	PUNCT
bracis-33554	135	1	\right	\right	PROPN
bracis-33554	135	2	)	)	PUNCT
bracis-33554	135	3	.	.	PUNCT
bracis-33554	136	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	136	2	(	(	PUNCT
bracis-33554	136	3	24	24	NUM
bracis-33554	136	4	)	)	PUNCT
bracis-33554	136	5	then	then	ADV
bracis-33554	136	6	the	the	DET
bracis-33554	136	7	sum	sum	NOUN
bracis-33554	136	8	for	for	ADP
bracis-33554	136	9	all	all	DET
bracis-33554	136	10	time	time	NOUN
bracis-33554	136	11	n	n	ADP
bracis-33554	136	12	of	of	ADP
bracis-33554	136	13	the	the	DET
bracis-33554	136	14	inverse	inverse	NOUN
bracis-33554	136	15	of	of	ADP
bracis-33554	136	16	\(u_{n}^{\pi	\(u_{n}^{\pi	NOUN
bracis-33554	136	17	,	,	PUNCT
bracis-33554	136	18	h}\	h}\	PROPN
bracis-33554	136	19	)	)	PUNCT
bracis-33554	136	20	is	be	AUX
bracis-33554	136	21	calculated	calculate	VERB
bracis-33554	136	22	and	and	CCONJ
bracis-33554	136	23	its	its	PRON
bracis-33554	136	24	average	average	NOUN
bracis-33554	136	25	is	be	AUX
bracis-33554	136	26	obtained	obtain	VERB
bracis-33554	136	27	when	when	SCONJ
bracis-33554	136	28	\(n\rightarrow	\(n\rightarrow	PROPN
bracis-33554	136	29	\infty	\infty	PROPN
bracis-33554	136	30	\	\	PROPN
bracis-33554	136	31	)	)	PUNCT
bracis-33554	136	32	 	 	SPACE
bracis-33554	136	33	by	by	ADP
bracis-33554	136	34	$	$	SYM
bracis-33554	136	35	$	$	SYM
bracis-33554	136	36	\begin{aligned	\begin{aligne	VERB
bracis-33554	136	37	}	}	PUNCT
bracis-33554	136	38	g^{\pi	g^{\pi	NOUN
bracis-33554	136	39	,	,	PUNCT
bracis-33554	136	40	h}_u	h}_u	NUM
bracis-33554	136	41	=	=	PUNCT
bracis-33554	136	42	\lim	\lim	NOUN
bracis-33554	136	43	_	_	PUNCT
bracis-33554	136	44	{	{	PUNCT
bracis-33554	136	45	n\rightarrow	n\rightarrow	NOUN
bracis-33554	136	46	\infty	\infty	VERB
bracis-33554	136	47	}	}	PUNCT
bracis-33554	136	48	\frac{1	\frac{1	ADV
bracis-33554	136	49	}	}	PUNCT
bracis-33554	136	50	{	{	PUNCT
bracis-33554	136	51	n	n	CCONJ
bracis-33554	136	52	}	}	PUNCT
bracis-33554	136	53	\sum	\sum	NOUN
bracis-33554	137	1	_	_	PUNCT
bracis-33554	137	2	{	{	PUNCT
bracis-33554	137	3	n=1}^{n	n=1}^{n	ADV
bracis-33554	137	4	}	}	PUNCT
bracis-33554	137	5	{	{	PUNCT
bracis-33554	137	6	u^{-1}(u^{\pi	u^{-1}(u^{\pi	NOUN
bracis-33554	137	7	,	,	PUNCT
bracis-33554	137	8	h}_{n	h}_{n	NOUN
bracis-33554	137	9	}	}	PUNCT
bracis-33554	137	10	)	)	PUNCT
bracis-33554	137	11	}	}	PUNCT
bracis-33554	137	12	.	.	PUNCT
bracis-33554	138	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	138	2	(	(	PUNCT
bracis-33554	138	3	25	25	NUM
bracis-33554	138	4	)	)	PUNCT
bracis-33554	138	5	for	for	ADP
bracis-33554	138	6	\(h=1\	\(h=1\	PROPN
bracis-33554	138	7	)	)	PUNCT
bracis-33554	138	8	and	and	CCONJ
bracis-33554	138	9	u	u	PRON
bracis-33554	138	10	being	be	AUX
bracis-33554	138	11	the	the	DET
bracis-33554	138	12	identity	identity	NOUN
bracis-33554	138	13	function	function	NOUN
bracis-33554	138	14	,	,	PUNCT
bracis-33554	138	15	eq	eq	NOUN
bracis-33554	138	16	.	.	PROPN
bracis-33554	138	17	 	 	SPACE
bracis-33554	138	18	25	25	NUM
bracis-33554	138	19	becomes	become	VERB
bracis-33554	138	20	the	the	DET
bracis-33554	138	21	risk	risk	NOUN
bracis-33554	138	22	-	-	PUNCT
bracis-33554	138	23	neutral	neutral	ADJ
bracis-33554	138	24	average	average	ADJ
bracis-33554	138	25	reward	reward	NOUN
bracis-33554	138	26	,	,	PUNCT
bracis-33554	138	27	equivalent	equivalent	ADJ
bracis-33554	138	28	to	to	ADP
bracis-33554	138	29	eq	eq	PROPN
bracis-33554	138	30	.	.	PUNCT
bracis-33554	138	31	 	 	SPACE
bracis-33554	139	1	2	2	X
bracis-33554	139	2	.	.	X
bracis-33554	139	3	note	note	VERB
bracis-33554	139	4	that	that	SCONJ
bracis-33554	139	5	in	in	ADP
bracis-33554	139	6	this	this	DET
bracis-33554	139	7	work	work	NOUN
bracis-33554	139	8	eq	eq	ADP
bracis-33554	139	9	.	.	PUNCT
bracis-33554	139	10	 	 	SPACE
bracis-33554	139	11	25	25	NUM
bracis-33554	139	12	is	be	AUX
bracis-33554	139	13	proposed	propose	VERB
bracis-33554	139	14	to	to	PART
bracis-33554	139	15	classify	classify	VERB
bracis-33554	139	16	existing	exist	VERB
bracis-33554	139	17	works	work	NOUN
bracis-33554	139	18	in	in	ADP
bracis-33554	139	19	the	the	DET
bracis-33554	139	20	literature	literature	NOUN
bracis-33554	139	21	concerning	concern	VERB
bracis-33554	139	22	h.	h.	PROPN
bracis-33554	139	23	when	when	SCONJ
bracis-33554	139	24	\(h=\infty	\(h=\infty	ADJ
bracis-33554	139	25	\	\	NOUN
bracis-33554	139	26	)	)	PUNCT
bracis-33554	139	27	,	,	PUNCT
bracis-33554	139	28	eq	eq	NOUN
bracis-33554	139	29	.	.	PROPN
bracis-33554	139	30	 	 	SPACE
bracis-33554	139	31	25	25	NUM
bracis-33554	139	32	is	be	AUX
bracis-33554	139	33	equivalent	equivalent	ADJ
bracis-33554	139	34	to	to	ADP
bracis-33554	139	35	the	the	DET
bracis-33554	139	36	criterion	criterion	NOUN
bracis-33554	139	37	used	use	VERB
bracis-33554	139	38	by	by	ADP
bracis-33554	139	39	howard	howard	PROPN
bracis-33554	139	40	and	and	CCONJ
bracis-33554	139	41	matheson	matheson	PROPN
bracis-33554	140	1	[	[	X
bracis-33554	140	2	2	2	NUM
bracis-33554	140	3	]	]	PUNCT
bracis-33554	140	4	.	.	PUNCT
bracis-33554	141	1	risk	risk	NOUN
bracis-33554	141	2	-	-	PUNCT
bracis-33554	141	3	sensitive	sensitive	ADJ
bracis-33554	141	4	criterion	criterion	NOUN
bracis-33554	141	5	with	with	ADP
bracis-33554	141	6	cvar	cvar	NOUN
bracis-33554	141	7	.	.	PUNCT
bracis-33554	142	1	equation	equation	NOUN
bracis-33554	142	2	 	 	SPACE
bracis-33554	142	3	26	26	NUM
bracis-33554	142	4	considers	consider	VERB
bracis-33554	142	5	the	the	DET
bracis-33554	142	6	average	average	ADJ
bracis-33554	142	7	cvar	cvar	NOUN
bracis-33554	142	8	of	of	ADP
bracis-33554	142	9	the	the	DET
bracis-33554	142	10	accumulated	accumulate	VERB
bracis-33554	142	11	reward	reward	NOUN
bracis-33554	142	12	.	.	PUNCT
bracis-33554	143	1	analogous	analogous	ADJ
bracis-33554	143	2	to	to	ADP
bracis-33554	143	3	eq	eq	PROPN
bracis-33554	143	4	.	.	PUNCT
bracis-33554	143	5	 	 	SPACE
bracis-33554	143	6	21	21	NUM
bracis-33554	143	7	,	,	PUNCT
bracis-33554	143	8	it	it	PRON
bracis-33554	143	9	considers	consider	VERB
bracis-33554	143	10	the	the	DET
bracis-33554	143	11	accumulated	accumulate	VERB
bracis-33554	143	12	reward	reward	NOUN
bracis-33554	143	13	of	of	ADP
bracis-33554	143	14	the	the	DET
bracis-33554	143	15	stochastic	stochastic	ADJ
bracis-33554	143	16	process	process	NOUN
bracis-33554	143	17	,	,	PUNCT
bracis-33554	143	18	but	but	CCONJ
bracis-33554	143	19	instead	instead	ADV
bracis-33554	143	20	of	of	ADP
bracis-33554	143	21	applying	apply	VERB
bracis-33554	143	22	the	the	DET
bracis-33554	143	23	utility	utility	NOUN
bracis-33554	143	24	function	function	NOUN
bracis-33554	143	25	u	u	NOUN
bracis-33554	143	26	,	,	PUNCT
bracis-33554	143	27	it	it	PRON
bracis-33554	143	28	applies	apply	VERB
bracis-33554	143	29	the	the	DET
bracis-33554	143	30	cvar	cvar	NOUN
bracis-33554	143	31	function	function	NOUN
bracis-33554	144	1	$	$	SYM
bracis-33554	144	2	$	$	SYM
bracis-33554	144	3	\begin{aligned	\begin{aligne	VERB
bracis-33554	144	4	}	}	PUNCT
bracis-33554	144	5	g^\pi	g^\pi	VERB
bracis-33554	144	6	_	_	PRON
bracis-33554	144	7	{	{	PUNCT
bracis-33554	144	8	\text	\text	ADJ
bracis-33554	144	9	{	{	PUNCT
bracis-33554	144	10	cvar	cvar	NOUN
bracis-33554	144	11	}	}	PUNCT
bracis-33554	144	12	}	}	PUNCT
bracis-33554	144	13	=	=	PUNCT
bracis-33554	144	14	\lim	\lim	NOUN
bracis-33554	144	15	_	_	PUNCT
bracis-33554	144	16	{	{	PUNCT
bracis-33554	144	17	n\rightarrow	n\rightarrow	NOUN
bracis-33554	144	18	\infty	\infty	PROPN
bracis-33554	144	19	}	}	PUNCT
bracis-33554	144	20	\frac{1}{n	\frac{1}{n	NOUN
bracis-33554	144	21	}	}	PUNCT
bracis-33554	144	22	\text	\text	ADV
bracis-33554	144	23	{	{	PUNCT
bracis-33554	144	24	cvar}\left	cvar}\left	NOUN
bracis-33554	144	25	[	[	PUNCT
bracis-33554	144	26	\sum	\sum	NOUN
bracis-33554	144	27	_	_	PUNCT
bracis-33554	144	28	{	{	PUNCT
bracis-33554	144	29	n=1}^{n	n=1}^{n	ADJ
bracis-33554	144	30	}	}	PUNCT
bracis-33554	144	31	r_{n	r_{n	PROPN
bracis-33554	144	32	}	}	PUNCT
bracis-33554	144	33	\right	\right	NOUN
bracis-33554	144	34	]	]	PUNCT
bracis-33554	144	35	.	.	PUNCT
bracis-33554	145	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	145	2	(	(	PUNCT
bracis-33554	145	3	26	26	NUM
bracis-33554	145	4	)	)	PUNCT
bracis-33554	145	5	as	as	ADV
bracis-33554	145	6	far	far	ADV
bracis-33554	145	7	as	as	SCONJ
bracis-33554	145	8	we	we	PRON
bracis-33554	145	9	know	know	VERB
bracis-33554	145	10	,	,	PUNCT
bracis-33554	145	11	there	there	PRON
bracis-33554	145	12	is	be	VERB
bracis-33554	145	13	no	no	DET
bracis-33554	145	14	work	work	NOUN
bracis-33554	145	15	in	in	ADP
bracis-33554	145	16	the	the	DET
bracis-33554	145	17	literature	literature	NOUN
bracis-33554	145	18	that	that	PRON
bracis-33554	145	19	solves	solve	VERB
bracis-33554	145	20	eq	eq	PROPN
bracis-33554	145	21	.	.	PUNCT
bracis-33554	145	22	 	 	SPACE
bracis-33554	145	23	26	26	NUM
bracis-33554	145	24	.	.	PUNCT
bracis-33554	146	1	similar	similar	ADJ
bracis-33554	146	2	to	to	ADP
bracis-33554	146	3	eq	eq	PROPN
bracis-33554	146	4	.	.	PUNCT
bracis-33554	146	5	 	 	SPACE
bracis-33554	146	6	23	23	NUM
bracis-33554	146	7	,	,	PUNCT
bracis-33554	146	8	but	but	CCONJ
bracis-33554	146	9	considering	consider	VERB
bracis-33554	146	10	the	the	DET
bracis-33554	146	11	cvar	cvar	NOUN
bracis-33554	146	12	instead	instead	ADV
bracis-33554	146	13	of	of	ADP
bracis-33554	146	14	the	the	DET
bracis-33554	146	15	utility	utility	NOUN
bracis-33554	146	16	function	function	NOUN
bracis-33554	146	17	u	u	NOUN
bracis-33554	146	18	,	,	PUNCT
bracis-33554	146	19	eq	eq	PROPN
bracis-33554	146	20	.	.	PROPN
bracis-33554	146	21	 	 	SPACE
bracis-33554	146	22	27	27	NUM
bracis-33554	146	23	considers	consider	VERB
bracis-33554	146	24	the	the	DET
bracis-33554	146	25	accumulated	accumulate	VERB
bracis-33554	146	26	rewards	reward	NOUN
bracis-33554	146	27	of	of	ADP
bracis-33554	146	28	fixed	fix	VERB
bracis-33554	146	29	-	-	PUNCT
bracis-33554	146	30	length	length	NOUN
bracis-33554	146	31	sequences	sequence	NOUN
bracis-33554	146	32	h	h	NOUN
bracis-33554	146	33	started	start	VERB
bracis-33554	146	34	at	at	ADP
bracis-33554	146	35	each	each	DET
bracis-33554	146	36	time	time	NOUN
bracis-33554	146	37	n	n	CCONJ
bracis-33554	146	38	and	and	CCONJ
bracis-33554	146	39	calculates	calculate	VERB
bracis-33554	146	40	the	the	DET
bracis-33554	146	41	average	average	NOUN
bracis-33554	146	42	of	of	ADP
bracis-33554	146	43	the	the	DET
bracis-33554	146	44	cvar	cvar	ADJ
bracis-33554	146	45	values	value	NOUN
bracis-33554	146	46	of	of	ADP
bracis-33554	146	47	all	all	DET
bracis-33554	146	48	these	these	DET
bracis-33554	146	49	sequences	sequence	NOUN
bracis-33554	146	50	:	:	PUNCT
bracis-33554	146	51	$	$	SYM
bracis-33554	146	52	$	$	SYM
bracis-33554	146	53	\begin{aligned	\begin{aligne	VERB
bracis-33554	146	54	}	}	PUNCT
bracis-33554	146	55	g^{\pi	g^{\pi	NOUN
bracis-33554	146	56	,	,	PUNCT
bracis-33554	146	57	h}_\text	h}_\text	CCONJ
bracis-33554	146	58	{	{	PUNCT
bracis-33554	146	59	cvar	cvar	NOUN
bracis-33554	146	60	}	}	PUNCT
bracis-33554	146	61	=	=	PUNCT
bracis-33554	146	62	\lim	\lim	NOUN
bracis-33554	146	63	_	_	PUNCT
bracis-33554	146	64	{	{	PUNCT
bracis-33554	146	65	n\rightarrow	n\rightarrow	NOUN
bracis-33554	146	66	\infty	\infty	PROPN
bracis-33554	146	67	}	}	PUNCT
bracis-33554	146	68	\frac{1}{n	\frac{1}{n	NOUN
bracis-33554	146	69	}	}	PUNCT
bracis-33554	147	1	\sum	\sum	NOUN
bracis-33554	147	2	_	_	PUNCT
bracis-33554	147	3	{	{	PUNCT
bracis-33554	147	4	n=1}^{n	n=1}^{n	ADV
bracis-33554	147	5	}	}	PUNCT
bracis-33554	147	6	\text	\text	ADV
bracis-33554	147	7	{	{	PUNCT
bracis-33554	147	8	cvar}\left	cvar}\left	NOUN
bracis-33554	147	9	[	[	PUNCT
bracis-33554	147	10	\sum	\sum	NOUN
bracis-33554	147	11	_	_	PUNCT
bracis-33554	147	12	{	{	PUNCT
bracis-33554	147	13	i	i	PROPN
bracis-33554	147	14	=	=	NOUN
bracis-33554	147	15	n}^{n+h-1	n}^{n+h-1	ADJ
bracis-33554	147	16	}	}	PUNCT
bracis-33554	147	17	r_{i	r_{i	NOUN
bracis-33554	147	18	}	}	PUNCT
bracis-33554	147	19	\right	\right	NOUN
bracis-33554	147	20	]	]	PUNCT
bracis-33554	147	21	.	.	PUNCT
bracis-33554	148	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	148	2	(	(	PUNCT
bracis-33554	148	3	27	27	NUM
bracis-33554	148	4	)	)	PUNCT
bracis-33554	148	5	equation	equation	NOUN
bracis-33554	148	6	 	 	SPACE
bracis-33554	148	7	28	28	NUM
bracis-33554	148	8	reinterprets	reinterpret	VERB
bracis-33554	148	9	eq	eq	PROPN
bracis-33554	148	10	.	.	PUNCT
bracis-33554	148	11	 	 	SPACE
bracis-33554	148	12	27	27	NUM
bracis-33554	148	13	by	by	ADP
bracis-33554	148	14	inserting	insert	VERB
bracis-33554	148	15	a	a	DET
bracis-33554	148	16	sequence	sequence	NOUN
bracis-33554	148	17	\(\psi	\(\psi	VERB
bracis-33554	148	18	\	\	NOUN
bracis-33554	148	19	)	)	PUNCT
bracis-33554	148	20	of	of	ADP
bracis-33554	148	21	h	h	NOUN
bracis-33554	148	22	states	state	NOUN
bracis-33554	148	23	,	,	PUNCT
bracis-33554	148	24	the	the	DET
bracis-33554	148	25	probability	probability	NOUN
bracis-33554	148	26	of	of	ADP
bracis-33554	148	27	this	this	DET
bracis-33554	148	28	sequence	sequence	NOUN
bracis-33554	148	29	of	of	ADP
bracis-33554	148	30	states	state	NOUN
bracis-33554	148	31	\(f_{s	\(f_{s	ADP
bracis-33554	148	32	,	,	PUNCT
bracis-33554	148	33	n}^	n}^	NOUN
bracis-33554	148	34	{	{	PUNCT
bracis-33554	148	35	\pi	\pi	PROPN
bracis-33554	148	36	,	,	PUNCT
bracis-33554	148	37	h}\	h}\	PROPN
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bracis-33554	148	39	(	(	PUNCT
bracis-33554	148	40	eq	eq	NOUN
bracis-33554	148	41	.	.	PUNCT
bracis-33554	148	42	 	 	SPACE
bracis-33554	148	43	19	19	NUM
bracis-33554	148	44	)	)	PUNCT
bracis-33554	148	45	and	and	CCONJ
bracis-33554	148	46	its	its	PRON
bracis-33554	148	47	accumulated	accumulate	VERB
bracis-33554	148	48	reward	reward	NOUN
bracis-33554	148	49	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	148	50	,	,	PUNCT
bracis-33554	148	51	h}_n(\psi	h}_n(\psi	VERB
bracis-33554	148	52	)	)	PUNCT
bracis-33554	148	53	\	\	PROPN
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bracis-33554	148	55	(	(	PUNCT
bracis-33554	148	56	eq	eq	NOUN
bracis-33554	148	57	.	.	PUNCT
bracis-33554	148	58	 	 	SPACE
bracis-33554	148	59	20	20	NUM
bracis-33554	148	60	)	)	PUNCT
bracis-33554	148	61	.	.	PUNCT
bracis-33554	149	1	thus	thus	ADV
bracis-33554	149	2	,	,	PUNCT
bracis-33554	149	3	for	for	ADP
bracis-33554	149	4	sequences	sequence	NOUN
bracis-33554	149	5	\(\psi	\(\psi	ADP
bracis-33554	149	6	\	\	NOUN
bracis-33554	149	7	)	)	PUNCT
bracis-33554	149	8	of	of	ADP
bracis-33554	149	9	size	size	NOUN
bracis-33554	149	10	h	h	NOUN
bracis-33554	149	11	starting	start	VERB
bracis-33554	149	12	at	at	ADP
bracis-33554	149	13	time	time	NOUN
bracis-33554	149	14	n	n	CCONJ
bracis-33554	149	15	:	:	PUNCT
bracis-33554	149	16	$	$	SYM
bracis-33554	149	17	$	$	SYM
bracis-33554	149	18	\begin{aligned	\begin{aligne	VERB
bracis-33554	149	19	}	}	PUNCT
bracis-33554	149	20	\begin{aligned	\begin{aligne	VERB
bracis-33554	149	21	}	}	PUNCT
bracis-33554	149	22	v_{\text	v_{\text	X
bracis-33554	149	23	{	{	PUNCT
bracis-33554	149	24	cvar},n}^{\pi	cvar},n}^{\pi	PROPN
bracis-33554	149	25	,	,	PUNCT
bracis-33554	149	26	h	h	NOUN
bracis-33554	149	27	}	}	PUNCT
bracis-33554	149	28	&	&	CCONJ
bracis-33554	149	29	=	=	SYM
bracis-33554	149	30	\text	\text	PROPN
bracis-33554	149	31	{	{	PUNCT
bracis-33554	149	32	cvar}_\alpha	cvar}_\alpha	PROPN
bracis-33554	149	33	(	(	PUNCT
bracis-33554	149	34	v^{\pi	v^{\pi	PROPN
bracis-33554	149	35	,	,	PUNCT
bracis-33554	149	36	h}_n(\psi	h}_n(\psi	VERB
bracis-33554	149	37	)	)	PUNCT
bracis-33554	149	38	)	)	PUNCT
bracis-33554	149	39	\\	\\	NOUN
bracis-33554	149	40	&	&	CCONJ
bracis-33554	149	41	=	=	PRON
bracis-33554	149	42	\text	\text	PROPN
bracis-33554	149	43	{	{	PUNCT
bracis-33554	149	44	var}_\alpha	var}_\alpha	PROPN
bracis-33554	149	45	(	(	PUNCT
bracis-33554	149	46	v^{\pi	v^{\pi	PROPN
bracis-33554	149	47	,	,	PUNCT
bracis-33554	149	48	h}_n(\psi	h}_n(\psi	VERB
bracis-33554	149	49	)	)	PUNCT
bracis-33554	149	50	)	)	PUNCT
bracis-33554	150	1	+	+	CCONJ
bracis-33554	150	2	\frac{1}{\alpha	\frac{1}{\alpha	ADJ
bracis-33554	150	3	}	}	PUNCT
bracis-33554	150	4	\sum	\sum	NOUN
bracis-33554	150	5	_	_	PRON
bracis-33554	150	6	{	{	PUNCT
bracis-33554	150	7	\psi	\psi	PROPN
bracis-33554	150	8	\in	\in	PROPN
bracis-33554	150	9	{	{	PUNCT
bracis-33554	150	10	s^h	s^h	NOUN
bracis-33554	150	11	}	}	PUNCT
bracis-33554	150	12	}	}	PUNCT
bracis-33554	150	13	f_{s	f_{s	PROPN
bracis-33554	150	14	,	,	PUNCT
bracis-33554	150	15	n}^{\pi	n}^{\pi	PROPN
bracis-33554	150	16	,	,	PUNCT
bracis-33554	150	17	h}(\psi	h}(\psi	NUM
bracis-33554	150	18	)	)	PUNCT
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bracis-33554	151	2	[	[	PUNCT
bracis-33554	151	3	{	{	PUNCT
bracis-33554	151	4	(	(	PUNCT
bracis-33554	151	5	v^{\pi	v^{\pi	PROPN
bracis-33554	151	6	,	,	PUNCT
bracis-33554	151	7	h}_n(\psi	h}_n(\psi	VERB
bracis-33554	151	8	)	)	PUNCT
bracis-33554	151	9	-\text	-\text	PROPN
bracis-33554	151	10	{	{	PUNCT
bracis-33554	151	11	var}_\alpha	var}_\alpha	PROPN
bracis-33554	151	12	(	(	PUNCT
bracis-33554	151	13	v^{\pi	v^{\pi	PROPN
bracis-33554	151	14	,	,	PUNCT
bracis-33554	151	15	h}_n(\psi	h}_n(\psi	PROPN
bracis-33554	151	16	)	)	PUNCT
bracis-33554	151	17	)	)	PUNCT
bracis-33554	151	18	)	)	PUNCT
bracis-33554	151	19	^{+	^{+	PUNCT
bracis-33554	151	20	}	}	PUNCT
bracis-33554	151	21	}	}	PUNCT
bracis-33554	151	22	_	_	PRON
bracis-33554	151	23	{	{	PUNCT
bracis-33554	151	24	}	}	PUNCT
bracis-33554	151	25	\,\right	\,\right	PROPN
bracis-33554	151	26	]	]	PUNCT
bracis-33554	151	27	.	.	PUNCT
bracis-33554	152	1	\end{aligned	\end{aligne	VERB
bracis-33554	152	2	}	}	PUNCT
bracis-33554	152	3	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	152	4	(	(	PUNCT
bracis-33554	152	5	28	28	NUM
bracis-33554	152	6	)	)	PUNCT
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bracis-33554	152	8	the	the	DET
bracis-33554	152	9	sum	sum	NOUN
bracis-33554	152	10	is	be	AUX
bracis-33554	152	11	calculated	calculate	VERB
bracis-33554	152	12	for	for	ADP
bracis-33554	152	13	all	all	DET
bracis-33554	152	14	time	time	NOUN
bracis-33554	152	15	n	n	CCONJ
bracis-33554	153	1	and	and	CCONJ
bracis-33554	153	2	then	then	ADV
bracis-33554	153	3	its	its	PRON
bracis-33554	153	4	average	average	NOUN
bracis-33554	153	5	is	be	AUX
bracis-33554	153	6	obtained	obtain	VERB
bracis-33554	153	7	for	for	ADP
bracis-33554	153	8	\(n\rightarrow	\(n\rightarrow	NOUN
bracis-33554	153	9	\infty	\infty	PROPN
bracis-33554	153	10	\	\	PROPN
bracis-33554	153	11	)	)	PUNCT
bracis-33554	153	12	$	$	SYM
bracis-33554	153	13	$	$	SYM
bracis-33554	153	14	\begin{aligned	\begin{aligne	VERB
bracis-33554	153	15	}	}	PUNCT
bracis-33554	153	16	g^{\pi	g^{\pi	NOUN
bracis-33554	153	17	,	,	PUNCT
bracis-33554	153	18	h}_{\text	h}_{\text	NOUN
bracis-33554	153	19	{	{	PUNCT
bracis-33554	153	20	cvar	cvar	NOUN
bracis-33554	153	21	}	}	PUNCT
bracis-33554	153	22	}	}	PUNCT
bracis-33554	153	23	=	=	PUNCT
bracis-33554	153	24	\lim	\lim	NOUN
bracis-33554	153	25	_	_	PUNCT
bracis-33554	153	26	{	{	PUNCT
bracis-33554	153	27	n\rightarrow	n\rightarrow	NOUN
bracis-33554	153	28	\infty	\infty	VERB
bracis-33554	153	29	}	}	PUNCT
bracis-33554	153	30	\frac{1	\frac{1	ADV
bracis-33554	153	31	}	}	PUNCT
bracis-33554	153	32	{	{	PUNCT
bracis-33554	153	33	n	n	CCONJ
bracis-33554	153	34	}	}	PUNCT
bracis-33554	153	35	\sum	\sum	NOUN
bracis-33554	153	36	_	_	PUNCT
bracis-33554	153	37	{	{	PUNCT
bracis-33554	153	38	n=1}^{n	n=1}^{n	ADJ
bracis-33554	153	39	}	}	PUNCT
bracis-33554	153	40	v^{\pi	v^{\pi	NOUN
bracis-33554	153	41	,	,	PUNCT
bracis-33554	153	42	h}_{\text	h}_{\text	NOUN
bracis-33554	153	43	{	{	PUNCT
bracis-33554	153	44	cvar},n	cvar},n	PROPN
bracis-33554	153	45	}	}	PUNCT
bracis-33554	153	46	.	.	PUNCT
bracis-33554	154	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	154	2	(	(	PUNCT
bracis-33554	154	3	29	29	NUM
bracis-33554	154	4	)	)	PUNCT
bracis-33554	154	5	note	note	VERB
bracis-33554	154	6	that	that	SCONJ
bracis-33554	154	7	in	in	ADP
bracis-33554	154	8	this	this	DET
bracis-33554	154	9	work	work	NOUN
bracis-33554	154	10	eq	eq	ADP
bracis-33554	154	11	.	.	PUNCT
bracis-33554	154	12	 	 	SPACE
bracis-33554	154	13	29	29	NUM
bracis-33554	154	14	is	be	AUX
bracis-33554	154	15	proposed	propose	VERB
bracis-33554	154	16	to	to	PART
bracis-33554	154	17	classify	classify	VERB
bracis-33554	154	18	existing	exist	VERB
bracis-33554	154	19	works	work	NOUN
bracis-33554	154	20	in	in	ADP
bracis-33554	154	21	the	the	DET
bracis-33554	154	22	literature	literature	NOUN
bracis-33554	154	23	concerning	concern	VERB
bracis-33554	154	24	h.	h.	PROPN
bracis-33554	154	25	when	when	SCONJ
bracis-33554	154	26	\(h=1\	\(h=1\	PROPN
bracis-33554	154	27	)	)	PUNCT
bracis-33554	154	28	,	,	PUNCT
bracis-33554	154	29	eq	eq	NOUN
bracis-33554	154	30	.	.	PUNCT
bracis-33554	154	31	 	 	SPACE
bracis-33554	154	32	28	28	NUM
bracis-33554	154	33	is	be	AUX
bracis-33554	154	34	equivalent	equivalent	ADJ
bracis-33554	154	35	to	to	ADP
bracis-33554	154	36	eq	eq	PROPN
bracis-33554	154	37	.	.	PUNCT
bracis-33554	154	38	 	 	SPACE
bracis-33554	154	39	14	14	NUM
bracis-33554	154	40	of	of	ADP
bracis-33554	154	41	xia	xia	PROPN
bracis-33554	154	42	and	and	CCONJ
bracis-33554	154	43	glynn	glynn	PROPN
bracis-33554	155	1	[	[	X
bracis-33554	155	2	7	7	NUM
bracis-33554	155	3	]	]	PUNCT
bracis-33554	155	4	.	.	PUNCT
bracis-33554	156	1	4	4	NUM
bracis-33554	156	2	numerical	numerical	PROPN
bracis-33554	156	3	example	example	NOUN
bracis-33554	156	4	example	example	NOUN
bracis-33554	156	5	1	1	NUM
bracis-33554	156	6	consider	consider	VERB
bracis-33554	156	7	an	an	DET
bracis-33554	156	8	mdp	mdp	NOUN
bracis-33554	156	9	with	with	ADP
bracis-33554	156	10	4	4	NUM
bracis-33554	156	11	states	state	NOUN
bracis-33554	156	12	and	and	CCONJ
bracis-33554	156	13	three	three	NUM
bracis-33554	156	14	policies	policy	NOUN
bracis-33554	156	15	\(\pi	\(\pi	ADP
bracis-33554	156	16	_	_	PRON
bracis-33554	156	17	1\	1\	NUM
bracis-33554	156	18	)	)	PUNCT
bracis-33554	156	19	,	,	PUNCT
bracis-33554	156	20	\(\pi	\(\pi	PROPN
bracis-33554	157	1	_	_	PUNCT
bracis-33554	157	2	2\	2\	X
bracis-33554	157	3	)	)	PUNCT
bracis-33554	157	4	and	and	CCONJ
bracis-33554	157	5	\(\pi	\(\pi	ADP
bracis-33554	157	6	_	_	NOUN
bracis-33554	158	1	3\	3\	NUM
bracis-33554	158	2	)	)	PUNCT
bracis-33554	158	3	,	,	PUNCT
bracis-33554	158	4	where	where	SCONJ
bracis-33554	158	5	the	the	DET
bracis-33554	158	6	transition	transition	NOUN
bracis-33554	158	7	matrix	matrix	NOUN
bracis-33554	158	8	of	of	ADP
bracis-33554	158	9	\(\pi	\(\pi	PROPN
bracis-33554	158	10	_	_	NOUN
bracis-33554	158	11	1\	1\	NUM
bracis-33554	158	12	)	)	PUNCT
bracis-33554	158	13	and	and	CCONJ
bracis-33554	158	14	\(\pi	\(\pi	ADP
bracis-33554	158	15	_	_	NOUN
bracis-33554	159	1	2\	2\	X
bracis-33554	159	2	)	)	PUNCT
bracis-33554	159	3	is	be	AUX
bracis-33554	159	4	$	$	SYM
bracis-33554	159	5	$	$	SYM
bracis-33554	159	6	\begin{aligned	\begin{aligne	VERB
bracis-33554	159	7	}	}	PUNCT
bracis-33554	159	8	p_{\pi	p_{\pi	NOUN
bracis-33554	159	9	_	_	NOUN
bracis-33554	159	10	1	1	NUM
bracis-33554	159	11	}	}	PUNCT
bracis-33554	159	12	=	=	PUNCT
bracis-33554	159	13	p_{\pi	p_{\pi	PROPN
bracis-33554	159	14	_	_	PRON
bracis-33554	159	15	2}=	2}=	NOUN
bracis-33554	159	16	\begin{bmatrix	\begin{bmatrix	NUM
bracis-33554	159	17	}	}	SYM
bracis-33554	159	18	0.5	0.5	NUM
bracis-33554	159	19	&	&	CCONJ
bracis-33554	159	20	0.5	0.5	NUM
bracis-33554	159	21	&	&	CCONJ
bracis-33554	159	22	0	0	NUM
bracis-33554	159	23	&	&	CCONJ
bracis-33554	159	24	0\\	0\\	NUM
bracis-33554	159	25	0	0	NUM
bracis-33554	159	26	&	&	CCONJ
bracis-33554	159	27	0	0	NUM
bracis-33554	159	28	&	&	CCONJ
bracis-33554	159	29	1	1	NUM
bracis-33554	159	30	&	&	CCONJ
bracis-33554	159	31	0\\	0\\	NUM
bracis-33554	159	32	0	0	NUM
bracis-33554	159	33	&	&	CCONJ
bracis-33554	159	34	0	0	NUM
bracis-33554	159	35	&	&	CCONJ
bracis-33554	159	36	0.5	0.5	NUM
bracis-33554	159	37	&	&	CCONJ
bracis-33554	159	38	0.5\\	0.5\\	NUM
bracis-33554	159	39	1	1	NUM
bracis-33554	159	40	&	&	CCONJ
bracis-33554	159	41	0	0	NUM
bracis-33554	159	42	&	&	CCONJ
bracis-33554	159	43	0	0	NUM
bracis-33554	159	44	&	&	CCONJ
bracis-33554	159	45	0	0	NUM
bracis-33554	159	46	\end{bmatrix	\end{bmatrix	NOUN
bracis-33554	159	47	}	}	PUNCT
bracis-33554	159	48	,	,	PUNCT
bracis-33554	159	49	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	159	50	(	(	PUNCT
bracis-33554	159	51	30	30	NUM
bracis-33554	159	52	)	)	PUNCT
bracis-33554	159	53	and	and	CCONJ
bracis-33554	159	54	the	the	DET
bracis-33554	159	55	transition	transition	NOUN
bracis-33554	159	56	matrix	matrix	NOUN
bracis-33554	159	57	for	for	ADP
bracis-33554	159	58	\(\pi	\(\pi	PROPN
bracis-33554	159	59	_	_	NOUN
bracis-33554	159	60	3\	3\	NUM
bracis-33554	159	61	)	)	PUNCT
bracis-33554	159	62	 	 	SPACE
bracis-33554	159	63	is	be	AUX
bracis-33554	159	64	$	$	SYM
bracis-33554	159	65	$	$	SYM
bracis-33554	159	66	\begin{aligned	\begin{aligne	VERB
bracis-33554	159	67	}	}	PUNCT
bracis-33554	159	68	p_{\pi	p_{\pi	NOUN
bracis-33554	159	69	_	_	NOUN
bracis-33554	159	70	3	3	NUM
bracis-33554	159	71	}	}	PUNCT
bracis-33554	159	72	=	=	PUNCT
bracis-33554	159	73	\begin{bmatrix	\begin{bmatrix	CCONJ
bracis-33554	159	74	}	}	PUNCT
bracis-33554	159	75	1	1	NUM
bracis-33554	159	76	&	&	CCONJ
bracis-33554	159	77	0	0	NUM
bracis-33554	159	78	&	&	CCONJ
bracis-33554	159	79	0	0	NUM
bracis-33554	159	80	&	&	CCONJ
bracis-33554	159	81	0\\	0\\	NUM
bracis-33554	159	82	0	0	NUM
bracis-33554	159	83	&	&	CCONJ
bracis-33554	159	84	0	0	PROPN
bracis-33554	159	85	&	&	CCONJ
bracis-33554	159	86	0	0	NUM
bracis-33554	159	87	&	&	CCONJ
bracis-33554	159	88	0\\	0\\	NUM
bracis-33554	159	89	0	0	NUM
bracis-33554	159	90	&	&	CCONJ
bracis-33554	159	91	0	0	PROPN
bracis-33554	159	92	&	&	CCONJ
bracis-33554	159	93	0	0	NUM
bracis-33554	159	94	&	&	CCONJ
bracis-33554	159	95	0\\	0\\	NUM
bracis-33554	159	96	0	0	NUM
bracis-33554	159	97	&	&	CCONJ
bracis-33554	159	98	0	0	PROPN
bracis-33554	159	99	&	&	CCONJ
bracis-33554	159	100	0	0	NUM
bracis-33554	159	101	&	&	CCONJ
bracis-33554	159	102	0	0	NUM
bracis-33554	159	103	\end{bmatrix	\end{bmatrix	NOUN
bracis-33554	159	104	}	}	PUNCT
bracis-33554	159	105	.	.	PUNCT
bracis-33554	160	1	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	160	2	(	(	PUNCT
bracis-33554	160	3	31	31	NUM
bracis-33554	160	4	)	)	PUNCT
bracis-33554	160	5	let	let	VERB
bracis-33554	160	6	\(r_{\pi	\(r_{\pi	NOUN
bracis-33554	160	7	}	}	PUNCT
bracis-33554	160	8	\	\	NOUN
bracis-33554	160	9	)	)	PUNCT
bracis-33554	160	10	be	be	AUX
bracis-33554	160	11	the	the	DET
bracis-33554	160	12	reward	reward	NOUN
bracis-33554	160	13	function	function	NOUN
bracis-33554	160	14	of	of	ADP
bracis-33554	160	15	policy	policy	NOUN
bracis-33554	160	16	\(\pi	\(\pi	ADP
bracis-33554	160	17	\	\	PROPN
bracis-33554	160	18	)	)	PUNCT
bracis-33554	160	19	,	,	PUNCT
bracis-33554	160	20	\(r_{\pi	\(r_{\pi	VERB
bracis-33554	160	21	_	_	NOUN
bracis-33554	160	22	1}=(0,6,0,-5)\	1}=(0,6,0,-5)\	NUM
bracis-33554	160	23	)	)	PUNCT
bracis-33554	160	24	,	,	PUNCT
bracis-33554	160	25	\(r_{\pi	\(r_{\pi	VERB
bracis-33554	160	26	_	_	PROPN
bracis-33554	160	27	2}=(0,1	2}=(0,1	NOUN
bracis-33554	160	28	,	,	PUNCT
bracis-33554	160	29	0,0)\	0,0)\	ADJ
bracis-33554	160	30	)	)	PUNCT
bracis-33554	160	31	and	and	CCONJ
bracis-33554	160	32	\(r_{\pi	\(r_{\pi	VERB
bracis-33554	160	33	_	_	PROPN
bracis-33554	160	34	3}=(\frac{1}{6})\	3}=(\frac{1}{6})\	NOUN
bracis-33554	160	35	)	)	PUNCT
bracis-33554	160	36	.	.	PUNCT
bracis-33554	161	1	figure	figure	NOUN
bracis-33554	161	2	 	 	SPACE
bracis-33554	161	3	1	1	NUM
bracis-33554	161	4	represents	represent	VERB
bracis-33554	161	5	the	the	DET
bracis-33554	161	6	three	three	NUM
bracis-33554	161	7	policies	policy	NOUN
bracis-33554	161	8	,	,	PUNCT
bracis-33554	161	9	where	where	SCONJ
bracis-33554	161	10	the	the	DET
bracis-33554	161	11	vertices	vertex	NOUN
bracis-33554	161	12	represent	represent	VERB
bracis-33554	161	13	the	the	DET
bracis-33554	161	14	states	state	NOUN
bracis-33554	161	15	,	,	PUNCT
bracis-33554	161	16	the	the	DET
bracis-33554	161	17	edges	edge	VERB
bracis-33554	161	18	the	the	DET
bracis-33554	161	19	actions	action	NOUN
bracis-33554	161	20	,	,	PUNCT
bracis-33554	161	21	and	and	CCONJ
bracis-33554	161	22	the	the	DET
bracis-33554	161	23	values	value	NOUN
bracis-33554	161	24	in	in	ADP
bracis-33554	161	25	parentheses	parenthesis	NOUN
bracis-33554	161	26	represent	represent	VERB
bracis-33554	161	27	the	the	DET
bracis-33554	161	28	transition	transition	NOUN
bracis-33554	161	29	probability	probability	NOUN
bracis-33554	161	30	and	and	CCONJ
bracis-33554	161	31	the	the	DET
bracis-33554	161	32	reward	reward	NOUN
bracis-33554	161	33	,	,	PUNCT
bracis-33554	161	34	respectively	respectively	ADV
bracis-33554	161	35	.	.	PUNCT
bracis-33554	162	1	the	the	DET
bracis-33554	162	2	markov	markov	NOUN
bracis-33554	162	3	chains	chain	NOUN
bracis-33554	162	4	generated	generate	VERB
bracis-33554	162	5	by	by	ADP
bracis-33554	162	6	the	the	DET
bracis-33554	162	7	stationary	stationary	ADJ
bracis-33554	162	8	policies	policy	NOUN
bracis-33554	162	9	in	in	ADP
bracis-33554	162	10	the	the	DET
bracis-33554	162	11	example	example	NOUN
bracis-33554	162	12	1	1	NUM
bracis-33554	162	13	are	be	AUX
bracis-33554	162	14	unichain	unichain	ADJ
bracis-33554	162	15	and	and	CCONJ
bracis-33554	162	16	aperiodic	aperiodic	ADJ
bracis-33554	162	17	.	.	PUNCT
bracis-33554	163	1	in	in	ADP
bracis-33554	163	2	this	this	DET
bracis-33554	163	3	way	way	NOUN
bracis-33554	163	4	,	,	PUNCT
bracis-33554	163	5	all	all	DET
bracis-33554	163	6	policies	policy	NOUN
bracis-33554	163	7	have	have	VERB
bracis-33554	163	8	a	a	DET
bracis-33554	163	9	constant	constant	ADJ
bracis-33554	163	10	gain	gain	NOUN
bracis-33554	163	11	,	,	PUNCT
bracis-33554	163	12	that	that	ADV
bracis-33554	163	13	is	is	ADV
bracis-33554	163	14	,	,	PUNCT
bracis-33554	163	15	the	the	DET
bracis-33554	163	16	gain	gain	NOUN
bracis-33554	163	17	of	of	ADP
bracis-33554	163	18	any	any	DET
bracis-33554	163	19	policy	policy	NOUN
bracis-33554	163	20	is	be	AUX
bracis-33554	163	21	independent	independent	ADJ
bracis-33554	163	22	of	of	ADP
bracis-33554	163	23	the	the	DET
bracis-33554	163	24	state	state	NOUN
bracis-33554	163	25	[	[	X
bracis-33554	163	26	4	4	NUM
bracis-33554	163	27	]	]	PUNCT
bracis-33554	163	28	.	.	PUNCT
bracis-33554	164	1	fig	fig	NOUN
bracis-33554	164	2	.	.	PUNCT
bracis-33554	165	1	1	1	X
bracis-33554	165	2	.	.	X
bracis-33554	165	3	graphical	graphical	ADJ
bracis-33554	165	4	representation	representation	NOUN
bracis-33554	165	5	of	of	ADP
bracis-33554	165	6	the	the	DET
bracis-33554	165	7	policies	policy	NOUN
bracis-33554	165	8	of	of	ADP
bracis-33554	165	9	the	the	DET
bracis-33554	165	10	mdp	mdp	NOUN
bracis-33554	165	11	given	give	VERB
bracis-33554	165	12	in	in	ADP
bracis-33554	165	13	example	example	NOUN
bracis-33554	165	14	1	1	NUM
bracis-33554	165	15	.	.	PUNCT
bracis-33554	165	16	full	full	ADJ
bracis-33554	165	17	size	size	NOUN
bracis-33554	165	18	image	image	NOUN
bracis-33554	165	19	the	the	DET
bracis-33554	165	20	steady	steady	ADJ
bracis-33554	165	21	-	-	PUNCT
bracis-33554	165	22	state	state	NOUN
bracis-33554	165	23	transition	transition	NOUN
bracis-33554	165	24	matrix	matrix	NOUN
bracis-33554	165	25	is	be	AUX
bracis-33554	165	26	calculated	calculate	VERB
bracis-33554	165	27	by	by	ADP
bracis-33554	165	28	\(p_\pi	\(p_\pi	NOUN
bracis-33554	165	29	^	^	NOUN
bracis-33554	165	30	*	*	PUNCT
bracis-33554	165	31	=	=	PUNCT
bracis-33554	165	32	\lim	\lim	NOUN
bracis-33554	165	33	_	_	PUNCT
bracis-33554	165	34	{	{	PUNCT
bracis-33554	165	35	n\rightarrow	n\rightarrow	NOUN
bracis-33554	165	36	\infty	\infty	VERB
bracis-33554	165	37	}	}	PUNCT
bracis-33554	165	38	p_\pi	p_\pi	NUM
bracis-33554	165	39	^{n+1}=p_\pi	^{n+1}=p_\pi	NOUN
bracis-33554	165	40	^np_\pi	^np_\pi	SYM
bracis-33554	165	41	\	\	PROPN
bracis-33554	165	42	)	)	PUNCT
bracis-33554	165	43	and	and	CCONJ
bracis-33554	165	44	for	for	ADP
bracis-33554	165	45	policies	policy	NOUN
bracis-33554	165	46	\(\pi	\(\pi	ADP
bracis-33554	165	47	_	_	PRON
bracis-33554	165	48	1\	1\	NUM
bracis-33554	165	49	)	)	PUNCT
bracis-33554	165	50	and	and	CCONJ
bracis-33554	165	51	\(\pi	\(\pi	ADP
bracis-33554	165	52	_	_	NOUN
bracis-33554	165	53	2\	2\	X
bracis-33554	165	54	)	)	PUNCT
bracis-33554	165	55	it	it	PRON
bracis-33554	165	56	 	 	SPACE
bracis-33554	165	57	is	be	AUX
bracis-33554	165	58	$	$	SYM
bracis-33554	165	59	$	$	SYM
bracis-33554	165	60	\begin{aligned	\begin{aligne	VERB
bracis-33554	165	61	}	}	PUNCT
bracis-33554	165	62	p_{\pi	p_{\pi	NOUN
bracis-33554	165	63	_	_	NOUN
bracis-33554	165	64	1}^	1}^	NUM
bracis-33554	165	65	*	*	PUNCT
bracis-33554	166	1	=	=	PUNCT
bracis-33554	166	2	p_{\pi	p_{\pi	PROPN
bracis-33554	166	3	_	_	PUNCT
bracis-33554	166	4	2}^	2}^	NUM
bracis-33554	166	5	*	*	PUNCT
bracis-33554	166	6	=	=	SYM
bracis-33554	166	7	\begin{bmatrix	\begin{bmatrix	X
bracis-33554	166	8	}	}	PUNCT
bracis-33554	166	9	\frac{1}{3	\frac{1}{3	PUNCT
bracis-33554	166	10	}	}	PUNCT
bracis-33554	166	11	&	&	CCONJ
bracis-33554	166	12	\frac{1}{6	\frac{1}{6	NOUN
bracis-33554	166	13	}	}	PUNCT
bracis-33554	166	14	&	&	CCONJ
bracis-33554	166	15	\frac{1}{3	\frac{1}{3	PRON
bracis-33554	166	16	}	}	PUNCT
bracis-33554	166	17	&	&	CCONJ
bracis-33554	166	18	\frac{1}{6}\\	\frac{1}{6}\\	PROPN
bracis-33554	166	19	\frac{1}{3	\frac{1}{3	NUM
bracis-33554	166	20	}	}	PUNCT
bracis-33554	166	21	&	&	CCONJ
bracis-33554	166	22	\frac{1}{6	\frac{1}{6	NOUN
bracis-33554	166	23	}	}	PUNCT
bracis-33554	166	24	&	&	CCONJ
bracis-33554	166	25	\frac{1}{3	\frac{1}{3	PRON
bracis-33554	166	26	}	}	PUNCT
bracis-33554	166	27	&	&	CCONJ
bracis-33554	166	28	\frac{1}{6}\\	\frac{1}{6}\\	PROPN
bracis-33554	166	29	\frac{1}{3	\frac{1}{3	NUM
bracis-33554	166	30	}	}	PUNCT
bracis-33554	166	31	&	&	CCONJ
bracis-33554	166	32	\frac{1}{6	\frac{1}{6	NOUN
bracis-33554	166	33	}	}	PUNCT
bracis-33554	166	34	&	&	CCONJ
bracis-33554	166	35	\frac{1}{3	\frac{1}{3	PRON
bracis-33554	166	36	}	}	PUNCT
bracis-33554	166	37	&	&	CCONJ
bracis-33554	166	38	\frac{1}{6}\\	\frac{1}{6}\\	PROPN
bracis-33554	166	39	\frac{1}{3	\frac{1}{3	NUM
bracis-33554	166	40	}	}	PUNCT
bracis-33554	166	41	&	&	CCONJ
bracis-33554	166	42	\frac{1}{6	\frac{1}{6	NOUN
bracis-33554	166	43	}	}	PUNCT
bracis-33554	166	44	&	&	CCONJ
bracis-33554	166	45	\frac{1}{3	\frac{1}{3	PRON
bracis-33554	166	46	}	}	PUNCT
bracis-33554	166	47	&	&	CCONJ
bracis-33554	166	48	\frac{1}{6	\frac{1}{6	NOUN
bracis-33554	166	49	}	}	PUNCT
bracis-33554	166	50	\end{bmatrix	\end{bmatrix	NOUN
bracis-33554	166	51	}	}	PUNCT
bracis-33554	166	52	.	.	PUNCT
bracis-33554	166	53	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-33554	166	54	(	(	PUNCT
bracis-33554	166	55	32	32	NUM
bracis-33554	166	56	)	)	PUNCT
bracis-33554	166	57	for	for	ADP
bracis-33554	166	58	\(\pi	\(\pi	PROPN
bracis-33554	166	59	_	_	NOUN
bracis-33554	166	60	3\	3\	NUM
bracis-33554	166	61	)	)	PUNCT
bracis-33554	166	62	,	,	PUNCT
bracis-33554	166	63	\(p^*_{\pi	\(p^*_{\pi	ADP
bracis-33554	166	64	_	_	NOUN
bracis-33554	166	65	3}=p_{\pi	3}=p_{\pi	NOUN
bracis-33554	167	1	_	_	NOUN
bracis-33554	167	2	3}\	3}\	NUM
bracis-33554	167	3	)	)	PUNCT
bracis-33554	167	4	.	.	PUNCT
bracis-33554	168	1	although	although	SCONJ
bracis-33554	168	2	the	the	DET
bracis-33554	168	3	policies	policy	NOUN
bracis-33554	168	4	\(\pi	\(\pi	ADP
bracis-33554	168	5	_	_	PRON
bracis-33554	168	6	1\	1\	NUM
bracis-33554	168	7	)	)	PUNCT
bracis-33554	168	8	and	and	CCONJ
bracis-33554	168	9	\(\pi	\(\pi	ADP
bracis-33554	168	10	_	_	NOUN
bracis-33554	168	11	2\	2\	X
bracis-33554	168	12	)	)	PUNCT
bracis-33554	168	13	,	,	PUNCT
bracis-33554	168	14	with	with	ADP
bracis-33554	168	15	the	the	DET
bracis-33554	168	16	same	same	ADJ
bracis-33554	168	17	transition	transition	NOUN
bracis-33554	168	18	matrix	matrix	NOUN
bracis-33554	168	19	,	,	PUNCT
bracis-33554	168	20	have	have	VERB
bracis-33554	168	21	the	the	DET
bracis-33554	168	22	same	same	ADJ
bracis-33554	168	23	expected	expect	VERB
bracis-33554	168	24	average	average	ADJ
bracis-33554	168	25	reward	reward	NOUN
bracis-33554	168	26	,	,	PUNCT
bracis-33554	168	27	the	the	DET
bracis-33554	168	28	distributions	distribution	NOUN
bracis-33554	168	29	of	of	ADP
bracis-33554	168	30	accumulated	accumulate	VERB
bracis-33554	168	31	rewards	reward	NOUN
bracis-33554	168	32	for	for	ADP
bracis-33554	168	33	policy	policy	NOUN
bracis-33554	168	34	\(\pi	\(\pi	PROPN
bracis-33554	168	35	_	_	NOUN
bracis-33554	168	36	1\	1\	NUM
bracis-33554	168	37	)	)	PUNCT
bracis-33554	168	38	have	have	VERB
bracis-33554	168	39	greater	great	ADJ
bracis-33554	168	40	variance	variance	NOUN
bracis-33554	168	41	than	than	ADP
bracis-33554	168	42	those	those	PRON
bracis-33554	168	43	for	for	ADP
bracis-33554	168	44	policy	policy	NOUN
bracis-33554	168	45	\(\pi	\(\pi	ADP
bracis-33554	168	46	_	_	PROPN
bracis-33554	168	47	2\	2\	X
bracis-33554	168	48	)	)	PUNCT
bracis-33554	168	49	for	for	ADP
bracis-33554	168	50	different	different	ADJ
bracis-33554	168	51	values	value	NOUN
bracis-33554	168	52	of	of	ADP
bracis-33554	168	53	h	h	NOUN
bracis-33554	168	54	,	,	PUNCT
bracis-33554	168	55	as	as	SCONJ
bracis-33554	168	56	shown	show	VERB
bracis-33554	168	57	in	in	ADP
bracis-33554	168	58	fig	fig	NOUN
bracis-33554	168	59	.	.	PUNCT
bracis-33554	168	60	 	 	SPACE
bracis-33554	169	1	2	2	NUM
bracis-33554	169	2	.	.	PUNCT
bracis-33554	169	3	therefore	therefore	ADV
bracis-33554	169	4	,	,	PUNCT
bracis-33554	169	5	risk	risk	NOUN
bracis-33554	169	6	-	-	PUNCT
bracis-33554	169	7	sensitive	sensitive	ADJ
bracis-33554	169	8	criteria	criterion	NOUN
bracis-33554	169	9	are	be	AUX
bracis-33554	169	10	expected	expect	VERB
bracis-33554	169	11	to	to	PART
bracis-33554	169	12	differentiate	differentiate	VERB
bracis-33554	169	13	between	between	ADP
bracis-33554	169	14	policies	policy	NOUN
bracis-33554	169	15	\(\pi	\(\pi	ADP
bracis-33554	169	16	_	_	NOUN
bracis-33554	169	17	1\	1\	NUM
bracis-33554	169	18	)	)	PUNCT
bracis-33554	169	19	and	and	CCONJ
bracis-33554	169	20	\(\pi	\(\pi	ADP
bracis-33554	169	21	_	_	NOUN
bracis-33554	169	22	2\	2\	X
bracis-33554	169	23	)	)	PUNCT
bracis-33554	169	24	.	.	PUNCT
bracis-33554	170	1	fig	fig	NOUN
bracis-33554	170	2	.	.	PUNCT
bracis-33554	171	1	2	2	X
bracis-33554	171	2	.	.	X
bracis-33554	171	3	graphs	graph	NOUN
bracis-33554	171	4	of	of	ADP
bracis-33554	171	5	the	the	DET
bracis-33554	171	6	distribution	distribution	NOUN
bracis-33554	171	7	of	of	ADP
bracis-33554	171	8	accumulated	accumulate	VERB
bracis-33554	171	9	reward	reward	NOUN
bracis-33554	171	10	and	and	CCONJ
bracis-33554	171	11	cumulative	cumulative	ADJ
bracis-33554	171	12	distribution	distribution	NOUN
bracis-33554	171	13	function	function	NOUN
bracis-33554	171	14	(	(	PUNCT
bracis-33554	171	15	cdf	cdf	PROPN
bracis-33554	171	16	)	)	PUNCT
bracis-33554	171	17	of	of	ADP
bracis-33554	171	18	accumulated	accumulate	VERB
bracis-33554	171	19	reward	reward	NOUN
bracis-33554	171	20	for	for	ADP
bracis-33554	171	21	different	different	ADJ
bracis-33554	171	22	values	value	NOUN
bracis-33554	171	23	of	of	ADP
bracis-33554	171	24	\	\	PROPN
bracis-33554	171	25	(	(	PUNCT
bracis-33554	171	26	h	h	NOUN
bracis-33554	171	27	\	\	PROPN
bracis-33554	171	28	)	)	PUNCT
bracis-33554	171	29	.	.	PUNCT
bracis-33554	172	1	full	full	ADJ
bracis-33554	172	2	size	size	NOUN
bracis-33554	172	3	image	image	NOUN
bracis-33554	172	4	figures	figure	NOUN
bracis-33554	172	5	 	 	SPACE
bracis-33554	172	6	2	2	NUM
bracis-33554	172	7	a	a	NOUN
bracis-33554	172	8	)	)	PUNCT
bracis-33554	172	9	,	,	PUNCT
bracis-33554	172	10	c	c	NOUN
bracis-33554	172	11	)	)	PUNCT
bracis-33554	172	12	,	,	PUNCT
bracis-33554	172	13	e	e	NOUN
bracis-33554	172	14	)	)	PUNCT
bracis-33554	172	15	and	and	CCONJ
bracis-33554	172	16	g	g	NOUN
bracis-33554	172	17	)	)	PUNCT
bracis-33554	172	18	show	show	VERB
bracis-33554	172	19	the	the	DET
bracis-33554	172	20	distribution	distribution	NOUN
bracis-33554	172	21	of	of	ADP
bracis-33554	172	22	the	the	DET
bracis-33554	172	23	accumulated	accumulate	VERB
bracis-33554	172	24	reward	reward	NOUN
bracis-33554	172	25	for	for	ADP
bracis-33554	172	26	policies	policy	NOUN
bracis-33554	172	27	\(\pi	\(\pi	ADP
bracis-33554	172	28	_	_	NOUN
bracis-33554	172	29	1\	1\	NUM
bracis-33554	172	30	)	)	PUNCT
bracis-33554	172	31	(	(	PUNCT
bracis-33554	172	32	blue	blue	ADJ
bracis-33554	172	33	bars	bar	NOUN
bracis-33554	172	34	)	)	PUNCT
bracis-33554	172	35	,	,	PUNCT
bracis-33554	173	1	\(\pi	\(\pi	PROPN
bracis-33554	173	2	_	_	NOUN
bracis-33554	173	3	2\	2\	X
bracis-33554	173	4	)	)	PUNCT
bracis-33554	173	5	(	(	PUNCT
bracis-33554	173	6	orange	orange	PROPN
bracis-33554	173	7	bars	bar	NOUN
bracis-33554	173	8	)	)	PUNCT
bracis-33554	173	9	and	and	CCONJ
bracis-33554	173	10	\(\pi	\(\pi	ADP
bracis-33554	173	11	_	_	NOUN
bracis-33554	173	12	3\	3\	NUM
bracis-33554	173	13	)	)	PUNCT
bracis-33554	173	14	(	(	PUNCT
bracis-33554	173	15	green	green	ADJ
bracis-33554	173	16	bars	bar	NOUN
bracis-33554	173	17	)	)	PUNCT
bracis-33554	173	18	of	of	ADP
bracis-33554	173	19	the	the	DET
bracis-33554	173	20	mdp	mdp	NOUN
bracis-33554	173	21	given	give	VERB
bracis-33554	173	22	in	in	ADP
bracis-33554	173	23	the	the	DET
bracis-33554	173	24	example	example	NOUN
bracis-33554	173	25	1	1	NUM
bracis-33554	173	26	for	for	ADP
bracis-33554	173	27	\(h	\(h	PROPN
bracis-33554	173	28	\in	\in	PROPN
bracis-33554	173	29	\{1,2,5,101\}\	\{1,2,5,101\}\	NOUN
bracis-33554	173	30	)	)	PUNCT
bracis-33554	173	31	,	,	PUNCT
bracis-33554	173	32	respectively	respectively	ADV
bracis-33554	173	33	.	.	PUNCT
bracis-33554	174	1	in	in	ADP
bracis-33554	174	2	addition	addition	NOUN
bracis-33554	174	3	to	to	ADP
bracis-33554	174	4	the	the	DET
bracis-33554	174	5	distributions	distribution	NOUN
bracis-33554	174	6	,	,	PUNCT
bracis-33554	174	7	the	the	DET
bracis-33554	174	8	values	value	NOUN
bracis-33554	174	9	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	174	10	,	,	PUNCT
bracis-33554	174	11	h}\	h}\	NUM
bracis-33554	174	12	)	)	PUNCT
bracis-33554	174	13	(	(	PUNCT
bracis-33554	174	14	red	red	ADJ
bracis-33554	174	15	line	line	NOUN
bracis-33554	174	16	)	)	PUNCT
bracis-33554	174	17	,	,	PUNCT
bracis-33554	174	18	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	174	19	,	,	PUNCT
bracis-33554	174	20	h}_{u_{1}}\	h}_{u_{1}}\	PROPN
bracis-33554	174	21	)	)	PUNCT
bracis-33554	174	22	(	(	PUNCT
bracis-33554	174	23	purple	purple	ADJ
bracis-33554	174	24	line	line	NOUN
bracis-33554	174	25	)	)	PUNCT
bracis-33554	174	26	,	,	PUNCT
bracis-33554	174	27	\(v^	\(v^	VERB
bracis-33554	174	28	{	{	PUNCT
bracis-33554	174	29	\pi	\pi	PROPN
bracis-33554	174	30	,	,	PUNCT
bracis-33554	174	31	h}_{\text	h}_{\text	NOUN
bracis-33554	174	32	{	{	PUNCT
bracis-33554	174	33	var}_{0.2}}\	var}_{0.2}}\	NOUN
bracis-33554	174	34	)	)	PUNCT
bracis-33554	174	35	(	(	PUNCT
bracis-33554	174	36	brown	brown	ADJ
bracis-33554	174	37	line	line	NOUN
bracis-33554	174	38	)	)	PUNCT
bracis-33554	174	39	and	and	CCONJ
bracis-33554	174	40	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	174	41	,	,	PUNCT
bracis-33554	174	42	h}_{\text	h}_{\text	NOUN
bracis-33554	174	43	{	{	PUNCT
bracis-33554	174	44	cvar}_{0.2}}\	cvar}_{0.2}}\	PROPN
bracis-33554	174	45	)	)	PUNCT
bracis-33554	174	46	(	(	PUNCT
bracis-33554	174	47	pink	pink	ADJ
bracis-33554	174	48	line	line	NOUN
bracis-33554	174	49	)	)	PUNCT
bracis-33554	174	50	are	be	AUX
bracis-33554	174	51	showed	show	VERB
bracis-33554	174	52	.	.	PUNCT
bracis-33554	175	1	the	the	DET
bracis-33554	175	2	accumulated	accumulate	VERB
bracis-33554	175	3	rewards	reward	NOUN
bracis-33554	175	4	for	for	ADP
bracis-33554	175	5	\(h=1\	\(h=1\	PROPN
bracis-33554	175	6	)	)	PUNCT
bracis-33554	175	7	and	and	CCONJ
bracis-33554	175	8	\(h=2\	\(h=2\	NOUN
bracis-33554	175	9	)	)	PUNCT
bracis-33554	175	10	range	range	NOUN
bracis-33554	175	11	from	from	ADP
bracis-33554	175	12	\(-5\	\(-5\	PROPN
bracis-33554	175	13	)	)	PUNCT
bracis-33554	175	14	to	to	ADP
bracis-33554	175	15	6	6	NUM
bracis-33554	175	16	for	for	ADP
bracis-33554	175	17	\(\pi	\(\pi	NOUN
bracis-33554	175	18	_	_	NOUN
bracis-33554	175	19	1\	1\	NUM
bracis-33554	175	20	)	)	PUNCT
bracis-33554	175	21	and	and	CCONJ
bracis-33554	175	22	range	range	VERB
bracis-33554	175	23	from	from	ADP
bracis-33554	175	24	0	0	NUM
bracis-33554	175	25	to	to	ADP
bracis-33554	175	26	1	1	NUM
bracis-33554	175	27	for	for	ADP
bracis-33554	175	28	\(\pi	\(\pi	PROPN
bracis-33554	175	29	_	_	NOUN
bracis-33554	175	30	2\	2\	NUM
bracis-33554	175	31	)	)	PUNCT
bracis-33554	175	32	.	.	PUNCT
bracis-33554	176	1	for	for	ADP
bracis-33554	176	2	\(h=5\	\(h=5\	PROPN
bracis-33554	176	3	)	)	PUNCT
bracis-33554	176	4	,	,	PUNCT
bracis-33554	176	5	the	the	DET
bracis-33554	176	6	accumulated	accumulate	VERB
bracis-33554	176	7	rewards	reward	NOUN
bracis-33554	176	8	range	range	VERB
bracis-33554	176	9	from	from	ADP
bracis-33554	176	10	\(-5\	\(-5\	PROPN
bracis-33554	176	11	)	)	PUNCT
bracis-33554	176	12	to	to	ADP
bracis-33554	176	13	7	7	NUM
bracis-33554	176	14	for	for	ADP
bracis-33554	176	15	\(\pi	\(\pi	NOUN
bracis-33554	176	16	_	_	NOUN
bracis-33554	176	17	1\	1\	NUM
bracis-33554	176	18	)	)	PUNCT
bracis-33554	176	19	and	and	CCONJ
bracis-33554	176	20	from	from	ADP
bracis-33554	176	21	0	0	NUM
bracis-33554	176	22	to	to	ADP
bracis-33554	176	23	2	2	NUM
bracis-33554	176	24	for	for	ADP
bracis-33554	176	25	\(\pi	\(\pi	PROPN
bracis-33554	176	26	_	_	NOUN
bracis-33554	176	27	2\	2\	NUM
bracis-33554	176	28	)	)	PUNCT
bracis-33554	176	29	.	.	PUNCT
bracis-33554	177	1	for	for	ADP
bracis-33554	177	2	\(h=101\	\(h=101\	PROPN
bracis-33554	177	3	)	)	PUNCT
bracis-33554	177	4	,	,	PUNCT
bracis-33554	177	5	the	the	DET
bracis-33554	177	6	accumulated	accumulate	VERB
bracis-33554	177	7	rewards	reward	NOUN
bracis-33554	177	8	range	range	VERB
bracis-33554	177	9	from	from	ADP
bracis-33554	177	10	\(-5\	\(-5\	PROPN
bracis-33554	177	11	)	)	PUNCT
bracis-33554	177	12	to	to	ADP
bracis-33554	177	13	30	30	NUM
bracis-33554	177	14	for	for	ADP
bracis-33554	177	15	\(\pi	\(\pi	NOUN
bracis-33554	177	16	_	_	NOUN
bracis-33554	177	17	1\	1\	NUM
bracis-33554	177	18	)	)	PUNCT
bracis-33554	177	19	and	and	CCONJ
bracis-33554	177	20	from	from	ADP
bracis-33554	177	21	0	0	NUM
bracis-33554	177	22	to	to	ADP
bracis-33554	177	23	25	25	NUM
bracis-33554	177	24	for	for	ADP
bracis-33554	177	25	\(\pi	\(\pi	PROPN
bracis-33554	177	26	_	_	NOUN
bracis-33554	177	27	2\	2\	NUM
bracis-33554	177	28	)	)	PUNCT
bracis-33554	177	29	.	.	PUNCT
bracis-33554	178	1	the	the	DET
bracis-33554	178	2	accumulated	accumulate	VERB
bracis-33554	178	3	reward	reward	NOUN
bracis-33554	178	4	for	for	ADP
bracis-33554	178	5	\(\pi	\(\pi	PROPN
bracis-33554	178	6	_	_	NOUN
bracis-33554	178	7	3\	3\	NUM
bracis-33554	178	8	)	)	PUNCT
bracis-33554	178	9	does	do	AUX
bracis-33554	178	10	not	not	PART
bracis-33554	178	11	vary	vary	VERB
bracis-33554	178	12	for	for	ADP
bracis-33554	178	13	each	each	DET
bracis-33554	178	14	h.	h.	NOUN
bracis-33554	178	15	it	it	PRON
bracis-33554	178	16	is	be	AUX
bracis-33554	178	17	expected	expect	VERB
bracis-33554	178	18	that	that	SCONJ
bracis-33554	178	19	a	a	DET
bracis-33554	178	20	risk	risk	NOUN
bracis-33554	178	21	-	-	PUNCT
bracis-33554	178	22	averse	averse	ADJ
bracis-33554	178	23	criterion	criterion	NOUN
bracis-33554	178	24	may	may	AUX
bracis-33554	178	25	consider	consider	VERB
bracis-33554	178	26	these	these	DET
bracis-33554	178	27	three	three	NUM
bracis-33554	178	28	policies	policy	NOUN
bracis-33554	178	29	differently	differently	ADV
bracis-33554	178	30	.	.	PUNCT
bracis-33554	179	1	additionally	additionally	ADV
bracis-33554	179	2	,	,	PUNCT
bracis-33554	179	3	when	when	SCONJ
bracis-33554	179	4	h	h	NOUN
bracis-33554	179	5	tends	tend	VERB
bracis-33554	179	6	to	to	PART
bracis-33554	179	7	infinity	infinity	VERB
bracis-33554	179	8	,	,	PUNCT
bracis-33554	179	9	all	all	DET
bracis-33554	179	10	accumulated	accumulate	VERB
bracis-33554	179	11	rewards	reward	NOUN
bracis-33554	179	12	tend	tend	VERB
bracis-33554	179	13	to	to	PART
bracis-33554	179	14	infinity	infinity	VERB
bracis-33554	179	15	(	(	PUNCT
bracis-33554	179	16	see	see	VERB
bracis-33554	179	17	figs	fig	NOUN
bracis-33554	179	18	.	.	PUNCT
bracis-33554	179	19	 	 	SPACE
bracis-33554	179	20	2	2	NUM
bracis-33554	179	21	a	a	NOUN
bracis-33554	179	22	)	)	PUNCT
bracis-33554	179	23	,	,	PUNCT
bracis-33554	179	24	c	c	NOUN
bracis-33554	179	25	)	)	PUNCT
bracis-33554	179	26	,	,	PUNCT
bracis-33554	179	27	e	e	NOUN
bracis-33554	179	28	)	)	PUNCT
bracis-33554	179	29	and	and	CCONJ
bracis-33554	179	30	g	g	NOUN
bracis-33554	179	31	)	)	PUNCT
bracis-33554	179	32	)	)	PUNCT
bracis-33554	179	33	.	.	PUNCT
bracis-33554	180	1	figures	figure	NOUN
bracis-33554	180	2	 	 	SPACE
bracis-33554	180	3	2	2	NUM
bracis-33554	180	4	b	b	NOUN
bracis-33554	180	5	)	)	PUNCT
bracis-33554	180	6	,	,	PUNCT
bracis-33554	180	7	d	d	NOUN
bracis-33554	180	8	)	)	PUNCT
bracis-33554	180	9	,	,	PUNCT
bracis-33554	180	10	f	f	X
bracis-33554	180	11	)	)	PUNCT
bracis-33554	180	12	,	,	PUNCT
bracis-33554	180	13	and	and	CCONJ
bracis-33554	180	14	h	h	X
bracis-33554	180	15	)	)	PUNCT
bracis-33554	180	16	show	show	VERB
bracis-33554	180	17	the	the	DET
bracis-33554	180	18	cumulative	cumulative	ADJ
bracis-33554	180	19	distribution	distribution	NOUN
bracis-33554	180	20	function	function	NOUN
bracis-33554	180	21	(	(	PUNCT
bracis-33554	180	22	cdf	cdf	PROPN
bracis-33554	180	23	)	)	PUNCT
bracis-33554	180	24	for	for	ADP
bracis-33554	180	25	policies	policy	NOUN
bracis-33554	180	26	with	with	ADP
bracis-33554	180	27	the	the	DET
bracis-33554	180	28	same	same	ADJ
bracis-33554	180	29	values	value	NOUN
bracis-33554	180	30	of	of	ADP
bracis-33554	180	31	h.	h.	NOUN
bracis-33554	180	32	for	for	ADP
bracis-33554	180	33	each	each	DET
bracis-33554	180	34	policy	policy	NOUN
bracis-33554	180	35	,	,	PUNCT
bracis-33554	180	36	the	the	DET
bracis-33554	180	37	cdfs	cdfs	PROPN
bracis-33554	180	38	are	be	AUX
bracis-33554	180	39	symmetric	symmetric	ADJ
bracis-33554	180	40	.	.	PUNCT
bracis-33554	181	1	the	the	DET
bracis-33554	181	2	median	median	NOUN
bracis-33554	181	3	of	of	ADP
bracis-33554	181	4	\(\pi	\(\pi	PROPN
bracis-33554	181	5	_	_	NOUN
bracis-33554	181	6	1\	1\	NUM
bracis-33554	181	7	)	)	PUNCT
bracis-33554	181	8	and	and	CCONJ
bracis-33554	181	9	\(\pi	\(\pi	ADP
bracis-33554	181	10	_	_	NOUN
bracis-33554	181	11	2\	2\	X
bracis-33554	181	12	)	)	PUNCT
bracis-33554	181	13	are	be	AUX
bracis-33554	181	14	the	the	DET
bracis-33554	181	15	same	same	ADJ
bracis-33554	181	16	for	for	ADP
bracis-33554	181	17	all	all	DET
bracis-33554	181	18	values	value	NOUN
bracis-33554	181	19	of	of	ADP
bracis-33554	181	20	h.	h.	PROPN
bracis-33554	181	21	in	in	ADP
bracis-33554	181	22	the	the	DET
bracis-33554	181	23	next	next	ADJ
bracis-33554	181	24	subsections	subsection	NOUN
bracis-33554	181	25	,	,	PUNCT
bracis-33554	181	26	examples	example	NOUN
bracis-33554	181	27	of	of	ADP
bracis-33554	181	28	the	the	DET
bracis-33554	181	29	gain	gain	NOUN
bracis-33554	181	30	calculation	calculation	NOUN
bracis-33554	181	31	for	for	ADP
bracis-33554	181	32	each	each	PRON
bracis-33554	181	33	of	of	ADP
bracis-33554	181	34	the	the	DET
bracis-33554	181	35	criteria	criterion	NOUN
bracis-33554	181	36	used	use	VERB
bracis-33554	181	37	are	be	AUX
bracis-33554	181	38	shown	show	VERB
bracis-33554	181	39	.	.	PUNCT
bracis-33554	182	1	consider	consider	VERB
bracis-33554	182	2	the	the	DET
bracis-33554	182	3	following	follow	VERB
bracis-33554	182	4	notation	notation	NOUN
bracis-33554	182	5	regarding	regard	VERB
bracis-33554	182	6	policies	policy	NOUN
bracis-33554	182	7	:	:	PUNCT
bracis-33554	182	8	\(a\succ	\(a\succ	PROPN
bracis-33554	182	9	b\	b\	NOUN
bracis-33554	182	10	)	)	PUNCT
bracis-33554	182	11	means	mean	VERB
bracis-33554	182	12	that	that	SCONJ
bracis-33554	182	13	the	the	DET
bracis-33554	182	14	decision	decision	NOUN
bracis-33554	182	15	-	-	PUNCT
bracis-33554	182	16	maker	maker	NOUN
bracis-33554	182	17	prefers	prefer	VERB
bracis-33554	182	18	a	a	DET
bracis-33554	182	19	to	to	ADP
bracis-33554	182	20	b	b	NOUN
bracis-33554	182	21	,	,	PUNCT
bracis-33554	182	22	\(a	\(a	NOUN
bracis-33554	182	23	\sim	\sim	NOUN
bracis-33554	182	24	b\	b\	NOUN
bracis-33554	182	25	)	)	PUNCT
bracis-33554	182	26	means	mean	VERB
bracis-33554	182	27	that	that	SCONJ
bracis-33554	182	28	the	the	DET
bracis-33554	182	29	decision	decision	NOUN
bracis-33554	182	30	-	-	PUNCT
bracis-33554	182	31	maker	maker	NOUN
bracis-33554	182	32	has	have	VERB
bracis-33554	182	33	an	an	DET
bracis-33554	182	34	equal	equal	ADJ
bracis-33554	182	35	preference	preference	NOUN
bracis-33554	182	36	for	for	ADP
bracis-33554	182	37	either	either	CCONJ
bracis-33554	182	38	a	a	PRON
bracis-33554	182	39	or	or	CCONJ
bracis-33554	182	40	b	b	NOUN
bracis-33554	182	41	and	and	CCONJ
bracis-33554	182	42	\(a\succeq	\(a\succeq	ADJ
bracis-33554	182	43	b\	b\	NOUN
bracis-33554	182	44	)	)	PUNCT
bracis-33554	182	45	means	mean	VERB
bracis-33554	182	46	that	that	SCONJ
bracis-33554	182	47	the	the	DET
bracis-33554	182	48	decision	decision	NOUN
bracis-33554	182	49	-	-	PUNCT
bracis-33554	182	50	maker	maker	NOUN
bracis-33554	182	51	prefers	prefer	NOUN
bracis-33554	182	52	or	or	CCONJ
bracis-33554	182	53	has	have	VERB
bracis-33554	182	54	an	an	DET
bracis-33554	182	55	equal	equal	ADJ
bracis-33554	182	56	preference	preference	NOUN
bracis-33554	182	57	for	for	ADP
bracis-33554	182	58	a	a	DET
bracis-33554	182	59	or	or	CCONJ
bracis-33554	182	60	b.	b.	NOUN
bracis-33554	182	61	4.1	4.1	NUM
bracis-33554	182	62	calculation	calculation	NOUN
bracis-33554	182	63	of	of	ADP
bracis-33554	182	64	gain	gain	NOUN
bracis-33554	182	65	using	use	VERB
bracis-33554	182	66	the	the	DET
bracis-33554	182	67	risk	risk	NOUN
bracis-33554	182	68	-	-	PUNCT
bracis-33554	182	69	neutral	neutral	ADJ
bracis-33554	182	70	criterion	criterion	NOUN
bracis-33554	182	71	the	the	DET
bracis-33554	182	72	gain	gain	NOUN
bracis-33554	182	73	of	of	ADP
bracis-33554	182	74	a	a	DET
bracis-33554	182	75	policy	policy	NOUN
bracis-33554	182	76	\(\pi	\(\pi	ADP
bracis-33554	182	77	\	\	NOUN
bracis-33554	182	78	)	)	PUNCT
bracis-33554	182	79	,	,	PUNCT
bracis-33554	182	80	defined	define	VERB
bracis-33554	182	81	in	in	ADP
bracis-33554	182	82	eq	eq	PROPN
bracis-33554	182	83	.	.	PUNCT
bracis-33554	182	84	 	 	SPACE
bracis-33554	182	85	15	15	NUM
bracis-33554	182	86	,	,	PUNCT
bracis-33554	182	87	can	can	AUX
bracis-33554	182	88	be	be	AUX
bracis-33554	182	89	calculated	calculate	VERB
bracis-33554	182	90	by	by	ADP
bracis-33554	182	91	dividing	divide	VERB
bracis-33554	182	92	the	the	DET
bracis-33554	182	93	accumulated	accumulate	VERB
bracis-33554	182	94	reward	reward	NOUN
bracis-33554	182	95	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	182	96	}	}	PUNCT
bracis-33554	182	97	_	_	PUNCT
bracis-33554	182	98	n\	n\	NOUN
bracis-33554	182	99	)	)	PUNCT
bracis-33554	182	100	by	by	ADP
bracis-33554	182	101	the	the	DET
bracis-33554	182	102	number	number	NOUN
bracis-33554	182	103	of	of	ADP
bracis-33554	182	104	steps	step	NOUN
bracis-33554	182	105	n	n	CCONJ
bracis-33554	182	106	,	,	PUNCT
bracis-33554	182	107	i.e.	i.e.	X
bracis-33554	182	108	,	,	PUNCT
bracis-33554	182	109	\(g^	\(g^	ADJ
bracis-33554	182	110	\pi	\pi	NOUN
bracis-33554	182	111	=	=	NOUN
bracis-33554	182	112	\lim	\lim	NOUN
bracis-33554	182	113	_	_	PUNCT
bracis-33554	182	114	{	{	PUNCT
bracis-33554	182	115	n\rightarrow	n\rightarrow	NOUN
bracis-33554	182	116	\infty	\infty	VERB
bracis-33554	182	117	}	}	PUNCT
bracis-33554	182	118	\frac{1}{n}v^{\pi	\frac{1}{n}v^{\pi	ADJ
bracis-33554	182	119	}	}	PUNCT
bracis-33554	182	120	_	_	PUNCT
bracis-33554	182	121	n\	n\	NOUN
bracis-33554	182	122	)	)	PUNCT
bracis-33554	182	123	.	.	PUNCT
bracis-33554	183	1	\(v_n^\pi	\(v_n^\pi	NOUN
bracis-33554	183	2	\	\	NOUN
bracis-33554	183	3	)	)	PUNCT
bracis-33554	183	4	can	can	AUX
bracis-33554	183	5	be	be	AUX
bracis-33554	183	6	calculated	calculate	VERB
bracis-33554	183	7	iteratively	iteratively	ADV
bracis-33554	183	8	by	by	ADP
bracis-33554	183	9	$	$	SYM
bracis-33554	183	10	$	$	SYM
bracis-33554	183	11	\begin{aligned	\begin{aligne	VERB
bracis-33554	183	12	}	}	PUNCT
bracis-33554	183	13	v^{\pi	v^{\pi	NOUN
bracis-33554	183	14	,	,	PUNCT
bracis-33554	183	15	n+1}=v^{\pi	n+1}=v^{\pi	PROPN
bracis-33554	183	16	,	,	PUNCT
bracis-33554	183	17	n}+p_\pi	n}+p_\pi	PROPN
bracis-33554	183	18	^nr_\pi	^nr_\pi	PROPN
bracis-33554	183	19	,	,	PUNCT
bracis-33554	183	20	\end{aligned}$$	\end{aligned}$$	X
bracis-33554	183	21	(	(	PUNCT
bracis-33554	183	22	33	33	NUM
bracis-33554	183	23	)	)	PUNCT
bracis-33554	183	24	where	where	SCONJ
bracis-33554	183	25	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	183	26	,	,	PUNCT
bracis-33554	183	27	0}\	0}\	NUM
bracis-33554	183	28	)	)	PUNCT
bracis-33554	183	29	is	be	AUX
bracis-33554	183	30	a	a	DET
bracis-33554	183	31	null	null	ADJ
bracis-33554	183	32	vector	vector	NOUN
bracis-33554	183	33	of	of	ADP
bracis-33554	183	34	size	size	NOUN
bracis-33554	183	35	|s|	|s|	PROPN
bracis-33554	183	36	and	and	CCONJ
bracis-33554	183	37	\(p_\pi	\(p_\pi	X
bracis-33554	183	38	^0	^0	PUNCT
bracis-33554	183	39	=	=	SYM
bracis-33554	183	40	i\	i\	PROPN
bracis-33554	183	41	)	)	PUNCT
bracis-33554	183	42	.	.	PUNCT
bracis-33554	184	1	using	use	VERB
bracis-33554	184	2	this	this	DET
bracis-33554	184	3	form	form	NOUN
bracis-33554	184	4	of	of	ADP
bracis-33554	184	5	calculation	calculation	NOUN
bracis-33554	184	6	for	for	ADP
bracis-33554	184	7	the	the	DET
bracis-33554	184	8	example	example	NOUN
bracis-33554	184	9	,	,	PUNCT
bracis-33554	184	10	the	the	DET
bracis-33554	184	11	gain	gain	NOUN
bracis-33554	184	12	of	of	ADP
bracis-33554	184	13	policies	policy	NOUN
bracis-33554	184	14	\(\pi	\(\pi	ADP
bracis-33554	184	15	_	_	NOUN
bracis-33554	184	16	1\	1\	NUM
bracis-33554	184	17	)	)	PUNCT
bracis-33554	184	18	,	,	PUNCT
bracis-33554	184	19	\(\pi	\(\pi	PROPN
bracis-33554	185	1	_	_	PUNCT
bracis-33554	185	2	2\	2\	X
bracis-33554	185	3	)	)	PUNCT
bracis-33554	185	4	and	and	CCONJ
bracis-33554	185	5	\(\pi	\(\pi	ADP
bracis-33554	185	6	_	_	NOUN
bracis-33554	186	1	3\	3\	NUM
bracis-33554	186	2	)	)	PUNCT
bracis-33554	186	3	is	be	AUX
bracis-33554	186	4	\(g^{\pi	\(g^{\pi	ADJ
bracis-33554	186	5	_	_	NOUN
bracis-33554	186	6	1	1	NUM
bracis-33554	186	7	}	}	PUNCT
bracis-33554	186	8	=	=	PUNCT
bracis-33554	186	9	g^{\pi	g^{\pi	NOUN
bracis-33554	186	10	_	_	NOUN
bracis-33554	186	11	2	2	X
bracis-33554	186	12	}	}	PUNCT
bracis-33554	186	13	=	=	PUNCT
bracis-33554	186	14	g^{\pi	g^{\pi	NOUN
bracis-33554	186	15	_	_	NOUN
bracis-33554	186	16	3	3	X
bracis-33554	186	17	}	}	PUNCT
bracis-33554	186	18	=	=	SYM
bracis-33554	186	19	(	(	PUNCT
bracis-33554	186	20	0.167	0.167	NUM
bracis-33554	186	21	,	,	PUNCT
bracis-33554	186	22	0.167	0.167	NUM
bracis-33554	186	23	,	,	PUNCT
bracis-33554	186	24	0.167	0.167	NUM
bracis-33554	186	25	,	,	PUNCT
bracis-33554	186	26	0.167)\	0.167)\	NOUN
bracis-33554	186	27	)	)	PUNCT
bracis-33554	186	28	.	.	PUNCT
bracis-33554	187	1	the	the	DET
bracis-33554	187	2	gain	gain	NOUN
bracis-33554	187	3	of	of	ADP
bracis-33554	187	4	a	a	DET
bracis-33554	187	5	policy	policy	NOUN
bracis-33554	187	6	defined	define	VERB
bracis-33554	187	7	in	in	ADP
bracis-33554	187	8	eq	eq	PROPN
bracis-33554	187	9	.	.	PUNCT
bracis-33554	187	10	 	 	SPACE
bracis-33554	187	11	17	17	NUM
bracis-33554	187	12	can	can	AUX
bracis-33554	187	13	be	be	AUX
bracis-33554	187	14	calculated	calculate	VERB
bracis-33554	187	15	by	by	ADP
bracis-33554	187	16	multiplying	multiply	VERB
bracis-33554	187	17	the	the	DET
bracis-33554	187	18	steady	steady	ADJ
bracis-33554	187	19	-	-	PUNCT
bracis-33554	187	20	state	state	NOUN
bracis-33554	187	21	matrix	matrix	NOUN
bracis-33554	187	22	\(p_\pi	\(p_\pi	PROPN
bracis-33554	187	23	^*\	^*\	NUM
bracis-33554	187	24	)	)	PUNCT
bracis-33554	187	25	by	by	ADP
bracis-33554	187	26	the	the	DET
bracis-33554	187	27	policy	policy	NOUN
bracis-33554	187	28	reward	reward	NOUN
bracis-33554	187	29	\(r_\pi	\(r_\pi	ADP
bracis-33554	187	30	\	\	PROPN
bracis-33554	187	31	)	)	PUNCT
bracis-33554	187	32	,	,	PUNCT
bracis-33554	187	33	i.e.	i.e.	X
bracis-33554	187	34	,	,	PUNCT
bracis-33554	187	35	\(g^{\pi	\(g^{\pi	ADJ
bracis-33554	187	36	}	}	PUNCT
bracis-33554	187	37	=	=	NOUN
bracis-33554	187	38	p_{\pi	p_{\pi	NOUN
bracis-33554	187	39	}	}	PUNCT
bracis-33554	187	40	^*r_{\pi	^*r_{\pi	NUM
bracis-33554	187	41	}	}	PUNCT
bracis-33554	187	42	\	\	NOUN
bracis-33554	187	43	)	)	PUNCT
bracis-33554	188	1	[	[	X
bracis-33554	188	2	4	4	NUM
bracis-33554	188	3	]	]	PUNCT
bracis-33554	188	4	.	.	PUNCT
bracis-33554	189	1	in	in	ADP
bracis-33554	189	2	the	the	DET
bracis-33554	189	3	example	example	NOUN
bracis-33554	189	4	using	use	VERB
bracis-33554	189	5	this	this	DET
bracis-33554	189	6	second	second	ADJ
bracis-33554	189	7	form	form	NOUN
bracis-33554	189	8	of	of	ADP
bracis-33554	189	9	calculation	calculation	NOUN
bracis-33554	189	10	,	,	PUNCT
bracis-33554	189	11	the	the	DET
bracis-33554	189	12	gain	gain	NOUN
bracis-33554	189	13	is	be	AUX
bracis-33554	189	14	\(g^{\pi	\(g^{\pi	ADJ
bracis-33554	189	15	_	_	NOUN
bracis-33554	189	16	1	1	NUM
bracis-33554	189	17	}	}	PUNCT
bracis-33554	189	18	=	=	PUNCT
bracis-33554	189	19	g^{\pi	g^{\pi	NOUN
bracis-33554	189	20	_	_	NOUN
bracis-33554	189	21	2	2	X
bracis-33554	189	22	}	}	PUNCT
bracis-33554	189	23	=	=	PUNCT
bracis-33554	189	24	g^{\pi	g^{\pi	NOUN
bracis-33554	189	25	_	_	NOUN
bracis-33554	189	26	3	3	X
bracis-33554	189	27	}	}	PUNCT
bracis-33554	189	28	=	=	SYM
bracis-33554	189	29	(	(	PUNCT
bracis-33554	189	30	0.167	0.167	NUM
bracis-33554	189	31	,	,	PUNCT
bracis-33554	189	32	0.167	0.167	NUM
bracis-33554	189	33	,	,	PUNCT
bracis-33554	189	34	0.167	0.167	NUM
bracis-33554	189	35	,	,	PUNCT
bracis-33554	189	36	0.167).\	0.167).\	NUM
bracis-33554	189	37	)	)	PUNCT
bracis-33554	189	38	note	note	VERB
bracis-33554	189	39	that	that	SCONJ
bracis-33554	189	40	,	,	PUNCT
bracis-33554	189	41	using	use	VERB
bracis-33554	189	42	the	the	DET
bracis-33554	189	43	risk	risk	NOUN
bracis-33554	189	44	-	-	PUNCT
bracis-33554	189	45	neutral	neutral	ADJ
bracis-33554	189	46	criterion	criterion	NOUN
bracis-33554	189	47	\(\pi	\(\pi	ADP
bracis-33554	189	48	_	_	PROPN
bracis-33554	189	49	3	3	NUM
bracis-33554	189	50	\sim	\sim	NOUN
bracis-33554	189	51	\pi	\pi	PROPN
bracis-33554	189	52	_	_	PROPN
bracis-33554	189	53	2	2	NUM
bracis-33554	189	54	\sim	\sim	NOUN
bracis-33554	189	55	\pi	\pi	PROPN
bracis-33554	189	56	_	_	NOUN
bracis-33554	189	57	1\	1\	NUM
bracis-33554	189	58	)	)	PUNCT
bracis-33554	189	59	.	.	PUNCT
bracis-33554	190	1	4.2	4.2	NUM
bracis-33554	190	2	calculation	calculation	NOUN
bracis-33554	190	3	of	of	ADP
bracis-33554	190	4	gain	gain	NOUN
bracis-33554	190	5	using	use	VERB
bracis-33554	190	6	utility	utility	NOUN
bracis-33554	190	7	function	function	NOUN
bracis-33554	190	8	with	with	ADP
bracis-33554	190	9	\(\gamma	\(\gamma	NOUN
bracis-33554	190	10	=	=	NOUN
bracis-33554	190	11	1\	1\	NUM
bracis-33554	190	12	)	)	PUNCT
bracis-33554	190	13	for	for	ADP
bracis-33554	190	14	\(h=1\	\(h=1\	NOUN
bracis-33554	190	15	)	)	PUNCT
bracis-33554	190	16	to	to	PART
bracis-33554	190	17	calculate	calculate	VERB
bracis-33554	190	18	the	the	DET
bracis-33554	190	19	gain	gain	NOUN
bracis-33554	190	20	\(g^{\pi	\(g^{\pi	ADP
bracis-33554	190	21	,	,	PUNCT
bracis-33554	190	22	h}_\text	h}_\text	CCONJ
bracis-33554	190	23	{	{	PUNCT
bracis-33554	190	24	u}\	u}\	PROPN
bracis-33554	190	25	)	)	PUNCT
bracis-33554	190	26	,	,	PUNCT
bracis-33554	190	27	it	it	PRON
bracis-33554	190	28	is	be	AUX
bracis-33554	190	29	necessary	necessary	ADJ
bracis-33554	190	30	to	to	PART
bracis-33554	190	31	calculate	calculate	VERB
bracis-33554	190	32	\(f_{s	\(f_{s	PROPN
bracis-33554	190	33	,	,	PUNCT
bracis-33554	190	34	n}^{\pi	n}^{\pi	PROPN
bracis-33554	190	35	,	,	PUNCT
bracis-33554	190	36	h}(\psi	h}(\psi	NUM
bracis-33554	190	37	)	)	PUNCT
bracis-33554	190	38	\	\	NOUN
bracis-33554	190	39	)	)	PUNCT
bracis-33554	191	1	(	(	PUNCT
bracis-33554	191	2	eq	eq	NOUN
bracis-33554	191	3	.	.	PUNCT
bracis-33554	191	4	 	 	SPACE
bracis-33554	191	5	19	19	NUM
bracis-33554	191	6	)	)	PUNCT
bracis-33554	191	7	which	which	PRON
bracis-33554	191	8	is	be	AUX
bracis-33554	191	9	the	the	DET
bracis-33554	191	10	probability	probability	NOUN
bracis-33554	191	11	of	of	ADP
bracis-33554	191	12	the	the	DET
bracis-33554	191	13	sequence	sequence	NOUN
bracis-33554	191	14	\(\psi	\(\psi	VERB
bracis-33554	191	15	\	\	NOUN
bracis-33554	191	16	)	)	PUNCT
bracis-33554	191	17	of	of	ADP
bracis-33554	191	18	size	size	NOUN
bracis-33554	191	19	h	h	NOUN
bracis-33554	191	20	occurring	occur	VERB
bracis-33554	191	21	with	with	ADP
bracis-33554	191	22	the	the	DET
bracis-33554	191	23	process	process	NOUN
bracis-33554	191	24	starting	start	VERB
bracis-33554	191	25	in	in	ADP
bracis-33554	191	26	state	state	NOUN
bracis-33554	191	27	s	s	NOUN
bracis-33554	191	28	and	and	CCONJ
bracis-33554	191	29	in	in	ADP
bracis-33554	191	30	time	time	NOUN
bracis-33554	191	31	n.	n.	NOUN
bracis-33554	191	32	it	it	PRON
bracis-33554	191	33	is	be	AUX
bracis-33554	191	34	also	also	ADV
bracis-33554	191	35	necessary	necessary	ADJ
bracis-33554	191	36	to	to	PART
bracis-33554	191	37	calculate	calculate	VERB
bracis-33554	191	38	\(v_{n}^{\pi	\(v_{n}^{\pi	PROPN
bracis-33554	191	39	,	,	PUNCT
bracis-33554	191	40	h}(\psi	h}(\psi	NUM
bracis-33554	191	41	)	)	PUNCT
bracis-33554	191	42	\	\	NOUN
bracis-33554	191	43	)	)	PUNCT
bracis-33554	191	44	(	(	PUNCT
bracis-33554	191	45	eq	eq	NOUN
bracis-33554	191	46	.	.	PUNCT
bracis-33554	191	47	 	 	SPACE
bracis-33554	191	48	20	20	NUM
bracis-33554	191	49	)	)	PUNCT
bracis-33554	191	50	which	which	PRON
bracis-33554	191	51	is	be	AUX
bracis-33554	191	52	the	the	DET
bracis-33554	191	53	accumulated	accumulate	VERB
bracis-33554	191	54	reward	reward	NOUN
bracis-33554	191	55	of	of	ADP
bracis-33554	191	56	the	the	DET
bracis-33554	191	57	sequence	sequence	NOUN
bracis-33554	191	58	\(\psi	\(\psi	VERB
bracis-33554	191	59	\	\	NOUN
bracis-33554	191	60	)	)	PUNCT
bracis-33554	191	61	and	and	CCONJ
bracis-33554	191	62	\(u(v^{\	\(u(v^{\	PROPN
bracis-33554	191	63	pi	pi	PROPN
bracis-33554	191	64	,	,	PUNCT
bracis-33554	191	65	h}_n(\psi	h}_n(\psi	VERB
bracis-33554	191	66	)	)	PUNCT
bracis-33554	191	67	)	)	PUNCT
bracis-33554	191	68	\	\	PROPN
bracis-33554	191	69	)	)	PUNCT
bracis-33554	191	70	.	.	PUNCT
bracis-33554	192	1	table	table	NOUN
bracis-33554	192	2	 	 	SPACE
bracis-33554	192	3	1	1	NUM
bracis-33554	192	4	shows	show	VERB
bracis-33554	192	5	the	the	DET
bracis-33554	192	6	sequences	sequence	NOUN
bracis-33554	192	7	\(\psi	\(\psi	VERB
bracis-33554	192	8	\	\	NOUN
bracis-33554	192	9	)	)	PUNCT
bracis-33554	192	10	of	of	ADP
bracis-33554	192	11	size	size	NOUN
bracis-33554	192	12	\(h=1\	\(h=1\	PROPN
bracis-33554	192	13	)	)	PUNCT
bracis-33554	192	14	for	for	ADP
bracis-33554	192	15	policy	policy	NOUN
bracis-33554	192	16	\(\pi	\(\pi	PROPN
bracis-33554	193	1	_	_	NOUN
bracis-33554	193	2	1\	1\	NUM
bracis-33554	193	3	)	)	PUNCT
bracis-33554	193	4	(	(	PUNCT
bracis-33554	193	5	column	column	NOUN
bracis-33554	193	6	1	1	NUM
bracis-33554	193	7	)	)	PUNCT
bracis-33554	193	8	,	,	PUNCT
bracis-33554	193	9	\(f_{s	\(f_{s	NOUN
bracis-33554	193	10	,	,	PUNCT
bracis-33554	193	11	n}^{\pi	n}^{\pi	PROPN
bracis-33554	193	12	_	_	PUNCT
bracis-33554	193	13	1,h=1	1,h=1	NUM
bracis-33554	193	14	}	}	PUNCT
bracis-33554	193	15	(	(	PUNCT
bracis-33554	193	16	\psi	\psi	PROPN
bracis-33554	193	17	)	)	PUNCT
bracis-33554	193	18	\	\	PROPN
bracis-33554	193	19	)	)	PUNCT
bracis-33554	193	20	(	(	PUNCT
bracis-33554	193	21	column	column	NOUN
bracis-33554	193	22	2	2	NUM
bracis-33554	193	23	)	)	PUNCT
bracis-33554	193	24	and	and	CCONJ
bracis-33554	193	25	\(v_{n}^{\pi	\(v_{n}^{\pi	VERB
bracis-33554	193	26	_	_	NOUN
bracis-33554	193	27	1,h=1}(\psi	1,h=1}(\psi	NUM
bracis-33554	193	28	)	)	PUNCT
bracis-33554	193	29	\	\	NOUN
bracis-33554	193	30	)	)	PUNCT
bracis-33554	193	31	(	(	PUNCT
bracis-33554	193	32	column	column	NOUN
bracis-33554	193	33	3	3	NUM
bracis-33554	193	34	)	)	PUNCT
bracis-33554	193	35	and	and	CCONJ
bracis-33554	193	36	\(u(v^{\pi	\(u(v^{\pi	NOUN
bracis-33554	193	37	,	,	PUNCT
bracis-33554	193	38	h}_n(\psi	h}_n(\psi	PROPN
bracis-33554	193	39	)	)	PUNCT
bracis-33554	193	40	)	)	PUNCT
bracis-33554	193	41	\	\	NOUN
bracis-33554	193	42	)	)	PUNCT
bracis-33554	193	43	(	(	PUNCT
bracis-33554	193	44	column	column	NOUN
bracis-33554	193	45	4	4	NUM
bracis-33554	193	46	)	)	PUNCT
bracis-33554	193	47	.	.	PUNCT
bracis-33554	194	1	for	for	ADP
bracis-33554	194	2	policy	policy	NOUN
bracis-33554	194	3	\(\pi	\(\pi	PROPN
bracis-33554	194	4	_	_	NOUN
bracis-33554	194	5	1\	1\	NUM
bracis-33554	194	6	)	)	PUNCT
bracis-33554	194	7	,	,	PUNCT
bracis-33554	194	8	\(u^{\pi	\(u^{\pi	NOUN
bracis-33554	194	9	_	_	NOUN
bracis-33554	194	10	1,h=1}_n=\frac{1}{3}*(-1)+\frac{1}{6}*(-0.002)+\frac{1}{3}*(-1)+\frac{1}{6}*(-148.413)=-25.403\	1,h=1}_n=\frac{1}{3}*(-1)+\frac{1}{6}*(-0.002)+\frac{1}{3}*(-1)+\frac{1}{6}*(-148.413)=-25.403\	NUM
bracis-33554	194	11	)	)	PUNCT
bracis-33554	194	12	(	(	PUNCT
bracis-33554	194	13	eq	eq	NOUN
bracis-33554	194	14	.	.	PUNCT
bracis-33554	194	15	 	 	SPACE
bracis-33554	194	16	24	24	NUM
bracis-33554	194	17	)	)	PUNCT
bracis-33554	194	18	is	be	AUX
bracis-33554	194	19	calculated	calculate	VERB
bracis-33554	194	20	.	.	PUNCT
bracis-33554	195	1	thus	thus	ADV
bracis-33554	195	2	,	,	PUNCT
bracis-33554	195	3	\(v^{\pi	\(v^{\pi	VERB
bracis-33554	195	4	_	_	NOUN
bracis-33554	195	5	1,h=1}_{n	1,h=1}_{n	NUM
bracis-33554	195	6	}	}	PUNCT
bracis-33554	195	7	=	=	NOUN
bracis-33554	195	8	u^{-1}(u^{\pi	u^{-1}(u^{\pi	NOUN
bracis-33554	195	9	,	,	PUNCT
bracis-33554	195	10	h=1}_{n	h=1}_{n	NUM
bracis-33554	195	11	}	}	PUNCT
bracis-33554	195	12	)	)	PUNCT
bracis-33554	196	1	=	=	SYM
bracis-33554	196	2	-3.235\	-3.235\	PROPN
bracis-33554	196	3	)	)	PUNCT
bracis-33554	196	4	and	and	CCONJ
bracis-33554	196	5	\(g^{h=1}_{u_1	\(g^{h=1}_{u_1	NOUN
bracis-33554	196	6	}	}	PUNCT
bracis-33554	196	7	=	=	SYM
bracis-33554	196	8	\frac{v^{\pi	\frac{v^{\pi	VERB
bracis-33554	196	9	,	,	PUNCT
bracis-33554	196	10	h=1}_{n}}{1	h=1}_{n}}{1	X
bracis-33554	196	11	}	}	PUNCT
bracis-33554	196	12	=	=	SYM
bracis-33554	196	13	-3.235\	-3.235\	PROPN
bracis-33554	196	14	)	)	PUNCT
bracis-33554	196	15	.	.	PUNCT
bracis-33554	197	1	for	for	ADP
bracis-33554	197	2	policy	policy	NOUN
bracis-33554	197	3	\(\pi	\(\pi	ADP
bracis-33554	197	4	_	_	PROPN
bracis-33554	197	5	2\	2\	X
bracis-33554	197	6	)	)	PUNCT
bracis-33554	197	7	,	,	PUNCT
bracis-33554	197	8	\(u^{\pi	\(u^{\pi	ADJ
bracis-33554	197	9	_	_	NOUN
bracis-33554	197	10	2,h=1}_n=\frac{5}{6}*(-1)+\frac{1}{6}*(-0.368	2,h=1}_n=\frac{5}{6}*(-1)+\frac{1}{6}*(-0.368	NUM
bracis-33554	197	11	)	)	PUNCT
bracis-33554	197	12	=	=	SYM
bracis-33554	197	13	\)0.895	\)0.895	PROPN
bracis-33554	197	14	.	.	PUNCT
bracis-33554	197	15	consequently	consequently	ADV
bracis-33554	197	16	\(v^{\pi	\(v^{\pi	VERB
bracis-33554	197	17	_	_	NOUN
bracis-33554	197	18	2,h=1}_{n}=u^{-1}(-0.895	2,h=1}_{n}=u^{-1}(-0.895	NUM
bracis-33554	197	19	)	)	PUNCT
bracis-33554	197	20	=	=	SYM
bracis-33554	197	21	0.111\	0.111\	PROPN
bracis-33554	197	22	)	)	PUNCT
bracis-33554	197	23	and	and	CCONJ
bracis-33554	197	24	\(g^{h=1}_{u_1}=0.111\	\(g^{h=1}_{u_1}=0.111\	NOUN
bracis-33554	197	25	)	)	PUNCT
bracis-33554	197	26	.	.	PUNCT
bracis-33554	198	1	for	for	ADP
bracis-33554	198	2	policy	policy	NOUN
bracis-33554	198	3	\(\pi	\(\pi	ADP
bracis-33554	198	4	_	_	PUNCT
bracis-33554	198	5	3\	3\	NUM
bracis-33554	198	6	)	)	PUNCT
bracis-33554	198	7	,	,	PUNCT
bracis-33554	198	8	\(u^{\pi	\(u^{\pi	ADJ
bracis-33554	198	9	_	_	NOUN
bracis-33554	198	10	3,h=1}_n=-0.846\	3,h=1}_n=-0.846\	NUM
bracis-33554	198	11	)	)	PUNCT
bracis-33554	198	12	and	and	CCONJ
bracis-33554	198	13	\(v^{\pi	\(v^{\pi	VERB
bracis-33554	198	14	_	_	PUNCT
bracis-33554	198	15	3,h=1}_{n}=g^{h=1	3,h=1}_{n}=g^{h=1	NUM
bracis-33554	198	16	}	}	SYM
bracis-33554	198	17	_	_	PRON
bracis-33554	198	18	{	{	PUNCT
bracis-33554	198	19	u_1}=0.167\	u_1}=0.167\	NOUN
bracis-33554	198	20	)	)	PUNCT
bracis-33554	198	21	.	.	PUNCT
bracis-33554	199	1	figure	figure	NOUN
bracis-33554	199	2	 	 	SPACE
bracis-33554	199	3	2a	2a	NUM
bracis-33554	199	4	)	)	PUNCT
bracis-33554	199	5	shows	show	VERB
bracis-33554	199	6	the	the	DET
bracis-33554	199	7	values	value	NOUN
bracis-33554	199	8	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	199	9	,	,	PUNCT
bracis-33554	199	10	h=1}_{u_{1}}\	h=1}_{u_{1}}\	PROPN
bracis-33554	199	11	)	)	PUNCT
bracis-33554	199	12	for	for	ADP
bracis-33554	199	13	the	the	DET
bracis-33554	199	14	three	three	NUM
bracis-33554	199	15	policies	policy	NOUN
bracis-33554	199	16	(	(	PUNCT
bracis-33554	199	17	purple	purple	ADJ
bracis-33554	199	18	vertical	vertical	ADJ
bracis-33554	199	19	lines	line	NOUN
bracis-33554	199	20	)	)	PUNCT
bracis-33554	199	21	,	,	PUNCT
bracis-33554	199	22	which	which	PRON
bracis-33554	199	23	are	be	AUX
bracis-33554	199	24	used	use	VERB
bracis-33554	199	25	to	to	PART
bracis-33554	199	26	calculate	calculate	VERB
bracis-33554	199	27	their	their	PRON
bracis-33554	199	28	respective	respective	ADJ
bracis-33554	199	29	gains	gain	NOUN
bracis-33554	199	30	.	.	PUNCT
bracis-33554	200	1	for	for	ADP
bracis-33554	200	2	\(h=1\	\(h=1\	PROPN
bracis-33554	200	3	)	)	PUNCT
bracis-33554	200	4	and	and	CCONJ
bracis-33554	200	5	\(\gamma	\(\gamma	X
bracis-33554	200	6	=	=	NOUN
bracis-33554	200	7	1\	1\	NUM
bracis-33554	200	8	)	)	PUNCT
bracis-33554	200	9	,	,	PUNCT
bracis-33554	200	10	\(\pi	\(\pi	PROPN
bracis-33554	200	11	_	_	NOUN
bracis-33554	200	12	3	3	NUM
bracis-33554	200	13	\succ	\succ	PROPN
bracis-33554	200	14	\pi	\pi	PROPN
bracis-33554	200	15	_	_	PROPN
bracis-33554	200	16	2	2	NUM
bracis-33554	200	17	\succ	\succ	PROPN
bracis-33554	200	18	\pi	\pi	PROPN
bracis-33554	200	19	_	_	NOUN
bracis-33554	200	20	1\	1\	NUM
bracis-33554	200	21	)	)	PUNCT
bracis-33554	200	22	.	.	PUNCT
bracis-33554	201	1	table	table	NOUN
bracis-33554	201	2	1	1	NUM
bracis-33554	201	3	.	.	PUNCT
bracis-33554	202	1	sequences	sequence	NOUN
bracis-33554	202	2	\(\psi	\(\psi	VERB
bracis-33554	202	3	\	\	NOUN
bracis-33554	202	4	)	)	PUNCT
bracis-33554	202	5	of	of	ADP
bracis-33554	202	6	size	size	NOUN
bracis-33554	202	7	\(h=1\	\(h=1\	PROPN
bracis-33554	202	8	)	)	PUNCT
bracis-33554	202	9	for	for	ADP
bracis-33554	202	10	policy	policy	NOUN
bracis-33554	202	11	\(\pi	\(\pi	PROPN
bracis-33554	203	1	_	_	NOUN
bracis-33554	203	2	1\	1\	NUM
bracis-33554	203	3	)	)	PUNCT
bracis-33554	203	4	,	,	PUNCT
bracis-33554	203	5	\(f_{s	\(f_{s	PROPN
bracis-33554	203	6	,	,	PUNCT
bracis-33554	203	7	n	n	CCONJ
bracis-33554	203	8	}	}	PUNCT
bracis-33554	203	9	^{\pi	^{\pi	NUM
bracis-33554	204	1	_	_	NOUN
bracis-33554	204	2	1,h=1}(\psi	1,h=1}(\psi	NUM
bracis-33554	204	3	)	)	PUNCT
bracis-33554	204	4	\	\	PROPN
bracis-33554	204	5	)	)	PUNCT
bracis-33554	204	6	,	,	PUNCT
bracis-33554	204	7	\(v_{n}^{\pi	\(v_{n}^{\pi	VERB
bracis-33554	204	8	_	_	PUNCT
bracis-33554	204	9	1,h}(\psi	1,h}(\psi	NUM
bracis-33554	204	10	)	)	PUNCT
bracis-33554	204	11	\	\	NOUN
bracis-33554	204	12	)	)	PUNCT
bracis-33554	204	13	and	and	CCONJ
bracis-33554	204	14	\(u(v_{n}^{\pi	\(u(v_{n}^{\pi	VERB
bracis-33554	204	15	_	_	NOUN
bracis-33554	204	16	1,h}(\psi	1,h}(\psi	NUM
bracis-33554	204	17	)	)	PUNCT
bracis-33554	204	18	)	)	PUNCT
bracis-33554	205	1	\).full	\).full	VERB
bracis-33554	205	2	size	size	NOUN
bracis-33554	205	3	table	table	NOUN
bracis-33554	205	4	4.3	4.3	NUM
bracis-33554	205	5	calculation	calculation	NOUN
bracis-33554	205	6	of	of	ADP
bracis-33554	205	7	gain	gain	NOUN
bracis-33554	205	8	using	use	VERB
bracis-33554	205	9	utility	utility	NOUN
bracis-33554	205	10	function	function	NOUN
bracis-33554	205	11	with	with	ADP
bracis-33554	205	12	\(\gamma	\(\gamma	NOUN
bracis-33554	206	1	=	=	NOUN
bracis-33554	206	2	1\	1\	NUM
bracis-33554	206	3	)	)	PUNCT
bracis-33554	206	4	for	for	ADP
bracis-33554	206	5	\(h=\infty	\(h=\infty	NUM
bracis-33554	206	6	\	\	NOUN
bracis-33554	206	7	)	)	PUNCT
bracis-33554	207	1	solving	solve	VERB
bracis-33554	207	2	the	the	DET
bracis-33554	207	3	system	system	NOUN
bracis-33554	207	4	of	of	ADP
bracis-33554	207	5	eqs	eqs	PROPN
bracis-33554	207	6	.	.	PUNCT
bracis-33554	207	7	 	 	SPACE
bracis-33554	207	8	9	9	NUM
bracis-33554	207	9	proposed	propose	VERB
bracis-33554	207	10	in	in	ADP
bracis-33554	207	11	[	[	X
bracis-33554	207	12	2	2	NUM
bracis-33554	207	13	]	]	PUNCT
bracis-33554	207	14	to	to	PART
bracis-33554	207	15	evaluate	evaluate	VERB
bracis-33554	207	16	policies	policy	NOUN
bracis-33554	207	17	,	,	PUNCT
bracis-33554	207	18	\({g}^{\pi	\({g}^{\pi	VERB
bracis-33554	207	19	_	_	PUNCT
bracis-33554	207	20	1}_u	1}_u	NOUN
bracis-33554	208	1	=	=	PRON
bracis-33554	208	2	{	{	PUNCT
bracis-33554	208	3	g}^{\pi	g}^{\pi	PROPN
bracis-33554	208	4	_	_	PUNCT
bracis-33554	208	5	2}_u	2}_u	NOUN
bracis-33554	208	6	=	=	PUNCT
bracis-33554	208	7	(	(	PUNCT
bracis-33554	208	8	0.157	0.157	NUM
bracis-33554	208	9	,	,	PUNCT
bracis-33554	208	10	0.157	0.157	NUM
bracis-33554	208	11	,	,	PUNCT
bracis-33554	208	12	0.157	0.157	NUM
bracis-33554	208	13	,	,	PUNCT
bracis-33554	208	14	0.157)\	0.157)\	NUM
bracis-33554	208	15	)	)	PUNCT
bracis-33554	209	1	and	and	CCONJ
bracis-33554	209	2	\({g}^{\pi	\({g}^{\pi	VERB
bracis-33554	209	3	_	_	NOUN
bracis-33554	209	4	3}_u=(0.167)\	3}_u=(0.167)\	NUM
bracis-33554	209	5	)	)	PUNCT
bracis-33554	209	6	.	.	PUNCT
bracis-33554	210	1	as	as	SCONJ
bracis-33554	210	2	stated	state	VERB
bracis-33554	210	3	previously	previously	ADV
bracis-33554	210	4	,	,	PUNCT
bracis-33554	210	5	\({g}^{\pi	\({g}^{\pi	ADJ
bracis-33554	210	6	}	}	PUNCT
bracis-33554	210	7	_	_	PUNCT
bracis-33554	210	8	u=	u=	NOUN
bracis-33554	210	9	{	{	PUNCT
bracis-33554	210	10	g}^{\pi	g}^{\pi	NOUN
bracis-33554	210	11	,	,	PUNCT
bracis-33554	210	12	h=\infty	h=\infty	ADJ
bracis-33554	210	13	}	}	PUNCT
bracis-33554	210	14	_	_	PUNCT
bracis-33554	210	15	u\	u\	PUNCT
bracis-33554	210	16	)	)	PUNCT
bracis-33554	210	17	for	for	ADP
bracis-33554	210	18	any	any	DET
bracis-33554	210	19	policy	policy	NOUN
bracis-33554	210	20	.	.	PUNCT
bracis-33554	211	1	note	note	VERB
bracis-33554	211	2	that	that	SCONJ
bracis-33554	211	3	\(g^{\pi	\(g^{\pi	ADP
bracis-33554	211	4	}	}	PUNCT
bracis-33554	211	5	_	_	PUNCT
bracis-33554	211	6	u	u	NOUN
bracis-33554	211	7	\le	\le	PROPN
bracis-33554	211	8	g^{\pi	g^{\pi	NOUN
bracis-33554	211	9	}	}	PUNCT
bracis-33554	211	10	\	\	NOUN
bracis-33554	211	11	)	)	PUNCT
bracis-33554	211	12	for	for	ADP
bracis-33554	211	13	any	any	PRON
bracis-33554	211	14	of	of	ADP
bracis-33554	211	15	the	the	DET
bracis-33554	211	16	policies	policy	NOUN
bracis-33554	211	17	,	,	PUNCT
bracis-33554	211	18	what	what	PRON
bracis-33554	211	19	is	be	AUX
bracis-33554	211	20	expected	expect	VERB
bracis-33554	211	21	of	of	ADP
bracis-33554	211	22	a	a	DET
bracis-33554	211	23	risk	risk	NOUN
bracis-33554	211	24	-	-	PUNCT
bracis-33554	211	25	averse	averse	ADJ
bracis-33554	211	26	agent	agent	NOUN
bracis-33554	211	27	,	,	PUNCT
bracis-33554	211	28	whose	whose	DET
bracis-33554	211	29	certainty	certainty	NOUN
bracis-33554	211	30	equivalent	equivalent	ADJ
bracis-33554	211	31	gain	gain	NOUN
bracis-33554	211	32	is	be	AUX
bracis-33554	211	33	less	less	ADJ
bracis-33554	211	34	than	than	ADP
bracis-33554	211	35	or	or	CCONJ
bracis-33554	211	36	equal	equal	ADJ
bracis-33554	211	37	to	to	ADP
bracis-33554	211	38	the	the	DET
bracis-33554	211	39	gain	gain	NOUN
bracis-33554	211	40	.	.	PUNCT
bracis-33554	212	1	\(g^{\pi	\(g^{\pi	ADJ
bracis-33554	212	2	,	,	PUNCT
bracis-33554	212	3	h}_{u}\	h}_{u}\	PROPN
bracis-33554	212	4	)	)	PUNCT
bracis-33554	212	5	were	be	AUX
bracis-33554	212	6	calculated	calculate	VERB
bracis-33554	212	7	for	for	ADP
bracis-33554	212	8	\(1\le	\(1\le	PROPN
bracis-33554	212	9	h	h	PROPN
bracis-33554	212	10	\le	\le	PROPN
bracis-33554	212	11	2000\	2000\	NUM
bracis-33554	212	12	)	)	PUNCT
bracis-33554	212	13	and	and	CCONJ
bracis-33554	212	14	policies	policy	NOUN
bracis-33554	212	15	\(\pi	\(\pi	ADP
bracis-33554	212	16	\in	\in	PROPN
bracis-33554	212	17	\{\pi	\{\pi	NOUN
bracis-33554	212	18	_	_	NOUN
bracis-33554	212	19	1	1	NUM
bracis-33554	212	20	,	,	PUNCT
bracis-33554	212	21	\pi	\pi	ADP
bracis-33554	212	22	_	_	NOUN
bracis-33554	212	23	2	2	NUM
bracis-33554	212	24	,	,	PUNCT
bracis-33554	212	25	\pi	\pi	ADP
bracis-33554	212	26	_	_	NOUN
bracis-33554	212	27	3\}\	3\}\	NUM
bracis-33554	212	28	)	)	PUNCT
bracis-33554	212	29	.	.	PUNCT
bracis-33554	213	1	as	as	SCONJ
bracis-33554	213	2	expected	expect	VERB
bracis-33554	213	3	\(g^{\pi	\(g^{\pi	PROPN
bracis-33554	213	4	,	,	PUNCT
bracis-33554	213	5	h}_{u}\	h}_{u}\	PROPN
bracis-33554	213	6	)	)	PUNCT
bracis-33554	213	7	approaches	approach	VERB
bracis-33554	213	8	\(g^{\pi	\(g^{\pi	ADP
bracis-33554	213	9	,	,	PUNCT
bracis-33554	213	10	h=\infty	h=\infty	ADJ
bracis-33554	213	11	}	}	PUNCT
bracis-33554	213	12	_	_	PRON
bracis-33554	213	13	{	{	PUNCT
bracis-33554	213	14	u}\	u}\	PROPN
bracis-33554	213	15	)	)	PUNCT
bracis-33554	213	16	as	as	ADP
bracis-33554	213	17	h	h	NOUN
bracis-33554	213	18	increases	increase	NOUN
bracis-33554	213	19	.	.	PUNCT
bracis-33554	214	1	the	the	DET
bracis-33554	214	2	value	value	NOUN
bracis-33554	214	3	of	of	ADP
bracis-33554	214	4	\(g^{\pi	\(g^{\pi	NOUN
bracis-33554	214	5	_	_	NOUN
bracis-33554	214	6	1,h=2000}_{u}=g^{\pi	1,h=2000}_{u}=g^{\pi	NUM
bracis-33554	214	7	_	_	X
bracis-33554	214	8	2,h=2000}_{u}=(0.155	2,h=2000}_{u}=(0.155	NUM
bracis-33554	214	9	,	,	PUNCT
bracis-33554	214	10	0.155	0.155	NUM
bracis-33554	214	11	,	,	PUNCT
bracis-33554	214	12	0.155	0.155	NUM
bracis-33554	214	13	,	,	PUNCT
bracis-33554	214	14	0.155)\	0.155)\	NUM
bracis-33554	214	15	)	)	PUNCT
bracis-33554	214	16	and	and	CCONJ
bracis-33554	214	17	\(g^{\pi	\(g^{\pi	ADP
bracis-33554	214	18	_	_	NOUN
bracis-33554	214	19	3,h=2000}_{u}=(0.167)\	3,h=2000}_{u}=(0.167)\	NUM
bracis-33554	214	20	)	)	PUNCT
bracis-33554	214	21	.	.	PUNCT
bracis-33554	215	1	for	for	ADP
bracis-33554	215	2	\(h=\infty	\(h=\infty	NUM
bracis-33554	215	3	\	\	NOUN
bracis-33554	215	4	)	)	PUNCT
bracis-33554	215	5	and	and	CCONJ
bracis-33554	215	6	\(\gamma	\(\gamma	X
bracis-33554	215	7	=	=	NOUN
bracis-33554	215	8	1\	1\	NUM
bracis-33554	215	9	)	)	PUNCT
bracis-33554	215	10	,	,	PUNCT
bracis-33554	215	11	\(\pi	\(\pi	PROPN
bracis-33554	215	12	_	_	NOUN
bracis-33554	215	13	3	3	NUM
bracis-33554	215	14	\succ	\succ	PROPN
bracis-33554	215	15	\pi	\pi	PROPN
bracis-33554	215	16	_	_	PROPN
bracis-33554	215	17	2	2	NUM
bracis-33554	215	18	\sim	\sim	NOUN
bracis-33554	215	19	\pi	\pi	PROPN
bracis-33554	215	20	_	_	NOUN
bracis-33554	215	21	1\	1\	NUM
bracis-33554	215	22	)	)	PUNCT
bracis-33554	215	23	.	.	PUNCT
bracis-33554	216	1	4.4	4.4	NUM
bracis-33554	216	2	calculation	calculation	NOUN
bracis-33554	216	3	of	of	ADP
bracis-33554	216	4	gain	gain	NOUN
bracis-33554	216	5	using	use	VERB
bracis-33554	216	6	cvar	cvar	NOUN
bracis-33554	216	7	with	with	ADP
bracis-33554	216	8	\(\alpha	\(\alpha	NOUN
bracis-33554	216	9	=	=	SYM
bracis-33554	216	10	0.2\	0.2\	ADJ
bracis-33554	216	11	)	)	PUNCT
bracis-33554	216	12	for	for	ADP
bracis-33554	216	13	\(h=1\	\(h=1\	NOUN
bracis-33554	216	14	)	)	PUNCT
bracis-33554	216	15	to	to	PART
bracis-33554	216	16	calculate	calculate	VERB
bracis-33554	216	17	the	the	DET
bracis-33554	216	18	gain	gain	NOUN
bracis-33554	216	19	\(g^{\pi	\(g^{\pi	ADP
bracis-33554	216	20	,	,	PUNCT
bracis-33554	216	21	h}_\text	h}_\text	CCONJ
bracis-33554	216	22	{	{	PUNCT
bracis-33554	216	23	cvar}\	cvar}\	PROPN
bracis-33554	216	24	)	)	PUNCT
bracis-33554	216	25	,	,	PUNCT
bracis-33554	216	26	it	it	PRON
bracis-33554	216	27	is	be	AUX
bracis-33554	216	28	necessary	necessary	ADJ
bracis-33554	216	29	to	to	PART
bracis-33554	216	30	calculate	calculate	VERB
bracis-33554	216	31	\(f_{s	\(f_{s	PROPN
bracis-33554	216	32	,	,	PUNCT
bracis-33554	216	33	n}^{\pi	n}^{\pi	PROPN
bracis-33554	216	34	,	,	PUNCT
bracis-33554	216	35	h}(\psi	h}(\psi	NUM
bracis-33554	216	36	)	)	PUNCT
bracis-33554	217	1	\	\	NOUN
bracis-33554	217	2	)	)	PUNCT
bracis-33554	217	3	(	(	PUNCT
bracis-33554	217	4	eq	eq	NOUN
bracis-33554	217	5	.	.	PUNCT
bracis-33554	217	6	 	 	SPACE
bracis-33554	217	7	19	19	NUM
bracis-33554	217	8	)	)	PUNCT
bracis-33554	217	9	,	,	PUNCT
bracis-33554	217	10	\(v_{n}^{\pi	\(v_{n}^{\pi	PROPN
bracis-33554	217	11	,	,	PUNCT
bracis-33554	217	12	h}(\psi	h}(\psi	NUM
bracis-33554	217	13	)	)	PUNCT
bracis-33554	217	14	\	\	NOUN
bracis-33554	217	15	)	)	PUNCT
bracis-33554	217	16	(	(	PUNCT
bracis-33554	217	17	eq	eq	NOUN
bracis-33554	217	18	.	.	PUNCT
bracis-33554	217	19	 	 	SPACE
bracis-33554	217	20	20	20	NUM
bracis-33554	217	21	)	)	PUNCT
bracis-33554	217	22	and	and	CCONJ
bracis-33554	217	23	the	the	DET
bracis-33554	217	24	distribution	distribution	NOUN
bracis-33554	217	25	of	of	ADP
bracis-33554	217	26	these	these	DET
bracis-33554	217	27	accumulated	accumulate	VERB
bracis-33554	217	28	rewards	reward	NOUN
bracis-33554	217	29	\(f_{v_{n}^{\pi	\(f_{v_{n}^{\pi	NOUN
bracis-33554	217	30	}	}	PUNCT
bracis-33554	217	31	}	}	PUNCT
bracis-33554	217	32	^{h}\	^{h}\	NUM
bracis-33554	217	33	)	)	PUNCT
bracis-33554	217	34	.	.	PUNCT
bracis-33554	218	1	table	table	NOUN
bracis-33554	218	2	 	 	SPACE
bracis-33554	218	3	1	1	NUM
bracis-33554	218	4	shows	show	VERB
bracis-33554	218	5	the	the	DET
bracis-33554	218	6	sequences	sequence	NOUN
bracis-33554	218	7	\(\psi	\(\psi	VERB
bracis-33554	218	8	\	\	NOUN
bracis-33554	218	9	)	)	PUNCT
bracis-33554	218	10	of	of	ADP
bracis-33554	218	11	size	size	NOUN
bracis-33554	218	12	\(h=1\	\(h=1\	PROPN
bracis-33554	218	13	)	)	PUNCT
bracis-33554	218	14	for	for	ADP
bracis-33554	218	15	policy	policy	NOUN
bracis-33554	218	16	\(\pi	\(\pi	PROPN
bracis-33554	219	1	_	_	NOUN
bracis-33554	219	2	1\	1\	NUM
bracis-33554	219	3	)	)	PUNCT
bracis-33554	219	4	(	(	PUNCT
bracis-33554	219	5	column	column	NOUN
bracis-33554	219	6	1	1	NUM
bracis-33554	219	7	)	)	PUNCT
bracis-33554	219	8	,	,	PUNCT
bracis-33554	219	9	\(f_{s	\(f_{s	NOUN
bracis-33554	219	10	,	,	PUNCT
bracis-33554	219	11	n}^{\pi	n}^{\pi	PROPN
bracis-33554	219	12	_	_	PUNCT
bracis-33554	219	13	1,h=1	1,h=1	NUM
bracis-33554	219	14	}	}	PUNCT
bracis-33554	219	15	(	(	PUNCT
bracis-33554	219	16	\psi	\psi	PROPN
bracis-33554	219	17	)	)	PUNCT
bracis-33554	219	18	\	\	PROPN
bracis-33554	219	19	)	)	PUNCT
bracis-33554	219	20	(	(	PUNCT
bracis-33554	219	21	column	column	NOUN
bracis-33554	219	22	2	2	NUM
bracis-33554	219	23	)	)	PUNCT
bracis-33554	219	24	and	and	CCONJ
bracis-33554	219	25	\(v_{n}^{\pi	\(v_{n}^{\pi	VERB
bracis-33554	219	26	_	_	NOUN
bracis-33554	219	27	1,h=1}(\psi	1,h=1}(\psi	NUM
bracis-33554	219	28	)	)	PUNCT
bracis-33554	219	29	\	\	NOUN
bracis-33554	219	30	)	)	PUNCT
bracis-33554	219	31	(	(	PUNCT
bracis-33554	219	32	column	column	NOUN
bracis-33554	219	33	3	3	NUM
bracis-33554	219	34	)	)	PUNCT
bracis-33554	219	35	.	.	PUNCT
bracis-33554	220	1	thus	thus	ADV
bracis-33554	220	2	,	,	PUNCT
bracis-33554	220	3	the	the	DET
bracis-33554	220	4	possible	possible	ADJ
bracis-33554	220	5	accumulated	accumulate	VERB
bracis-33554	220	6	rewards	reward	NOUN
bracis-33554	220	7	are	be	AUX
bracis-33554	220	8	\((-5,0,6)\	\((-5,0,6)\	VERB
bracis-33554	220	9	)	)	PUNCT
bracis-33554	220	10	with	with	ADP
bracis-33554	220	11	distribution	distribution	NOUN
bracis-33554	220	12	\(f_{v^{\pi	\(f_{v^{\pi	NOUN
bracis-33554	220	13	_	_	PROPN
bracis-33554	220	14	1}_n}^{h=1}=(\frac{1}{6	1}_n}^{h=1}=(\frac{1}{6	PROPN
bracis-33554	220	15	}	}	PUNCT
bracis-33554	220	16	,	,	PUNCT
bracis-33554	220	17	\frac{4}{6	\frac{4}{6	PROPN
bracis-33554	220	18	}	}	PUNCT
bracis-33554	220	19	,	,	PUNCT
bracis-33554	220	20	\frac{1}{6})\	\frac{1}{6})\	NOUN
bracis-33554	220	21	)	)	PUNCT
bracis-33554	220	22	.	.	PUNCT
bracis-33554	221	1	considering	consider	VERB
bracis-33554	221	2	a	a	DET
bracis-33554	221	3	confidence	confidence	NOUN
bracis-33554	221	4	level	level	NOUN
bracis-33554	221	5	of	of	ADP
bracis-33554	221	6	\(20\%\	\(20\%\	NUM
bracis-33554	221	7	)	)	PUNCT
bracis-33554	221	8	,	,	PUNCT
bracis-33554	221	9	\(v^{\pi	\(v^{\pi	VERB
bracis-33554	221	10	_	_	NOUN
bracis-33554	221	11	1,h=1}_{\text	1,h=1}_{\text	NUM
bracis-33554	221	12	{	{	PUNCT
bracis-33554	221	13	var}_{0.2}}=\text	var}_{0.2}}=\text	X
bracis-33554	221	14	{	{	PUNCT
bracis-33554	221	15	var}_{0.2}(v_{n	var}_{0.2}(v_{n	PROPN
bracis-33554	221	16	}	}	PUNCT
bracis-33554	221	17	^{\pi	^{\pi	NUM
bracis-33554	222	1	_	_	X
bracis-33554	222	2	1,h=1})=0\	1,h=1})=0\	NUM
bracis-33554	222	3	)	)	PUNCT
bracis-33554	222	4	and	and	CCONJ
bracis-33554	222	5	\(v^{\pi	\(v^{\pi	VERB
bracis-33554	222	6	_	_	PROPN
bracis-33554	222	7	1,h=1}_{\text	1,h=1}_{\text	NUM
bracis-33554	222	8	{	{	PUNCT
bracis-33554	222	9	cvar}_{0.2}}=\text	cvar}_{0.2}}=\text	X
bracis-33554	222	10	{	{	PUNCT
bracis-33554	222	11	cvar}_{0.2}(v_{n}^{\pi	cvar}_{0.2}(v_{n}^{\pi	VERB
bracis-33554	222	12	_	_	NOUN
bracis-33554	222	13	1,h=1	1,h=1	NUM
bracis-33554	222	14	}	}	PUNCT
bracis-33554	222	15	)	)	PUNCT
bracis-33554	223	1	=	=	NOUN
bracis-33554	223	2	\frac{\frac{1}{6}(-5)+(0.2-\frac{1}{6})*0}{0.2}=-4.167\	\frac{\frac{1}{6}(-5)+(0.2-\frac{1}{6})*0}{0.2}=-4.167\	NOUN
bracis-33554	223	3	)	)	PUNCT
bracis-33554	223	4	.	.	PUNCT
bracis-33554	224	1	thus	thus	ADV
bracis-33554	224	2	,	,	PUNCT
bracis-33554	224	3	\(g^{\pi	\(g^{\pi	PROPN
bracis-33554	224	4	_	_	NOUN
bracis-33554	224	5	1,h=1}_{\text	1,h=1}_{\text	NUM
bracis-33554	224	6	{	{	PUNCT
bracis-33554	224	7	cvar}_{0.2	cvar}_{0.2	NOUN
bracis-33554	224	8	}	}	PUNCT
bracis-33554	224	9	}	}	PUNCT
bracis-33554	225	1	=	=	PUNCT
bracis-33554	225	2	\frac{v^{\pi	\frac{v^{\pi	VERB
bracis-33554	225	3	_	_	NOUN
bracis-33554	225	4	1,h=1}_{\text	1,h=1}_{\text	NUM
bracis-33554	225	5	{	{	PUNCT
bracis-33554	225	6	cvar}_{0.2	cvar}_{0.2	NOUN
bracis-33554	225	7	}	}	PUNCT
bracis-33554	225	8	}	}	PUNCT
bracis-33554	225	9	}	}	PUNCT
bracis-33554	225	10	{	{	PUNCT
bracis-33554	225	11	1	1	NUM
bracis-33554	225	12	}	}	PUNCT
bracis-33554	225	13	=	=	SYM
bracis-33554	225	14	-4,167\	-4,167\	NOUN
bracis-33554	225	15	)	)	PUNCT
bracis-33554	225	16	.	.	PUNCT
bracis-33554	226	1	for	for	ADP
bracis-33554	226	2	policy	policy	NOUN
bracis-33554	226	3	\(\pi	\(\pi	ADP
bracis-33554	226	4	_	_	PROPN
bracis-33554	226	5	2\	2\	X
bracis-33554	226	6	)	)	PUNCT
bracis-33554	226	7	,	,	PUNCT
bracis-33554	226	8	the	the	DET
bracis-33554	226	9	possible	possible	ADJ
bracis-33554	226	10	cumulative	cumulative	ADJ
bracis-33554	226	11	rewards	reward	NOUN
bracis-33554	226	12	are	be	AUX
bracis-33554	226	13	(	(	PUNCT
bracis-33554	226	14	0	0	NUM
bracis-33554	226	15	,	,	PUNCT
bracis-33554	226	16	 	 	SPACE
bracis-33554	226	17	1	1	NUM
bracis-33554	226	18	)	)	PUNCT
bracis-33554	226	19	with	with	ADP
bracis-33554	226	20	distribution	distribution	NOUN
bracis-33554	226	21	\(f_{v_{n}^{\pi	\(f_{v_{n}^{\pi	NOUN
bracis-33554	226	22	_	_	NOUN
bracis-33554	226	23	2}}^{h=1}=(\frac{5}{6	2}}^{h=1}=(\frac{5}{6	NUM
bracis-33554	226	24	}	}	PUNCT
bracis-33554	226	25	,	,	PUNCT
bracis-33554	226	26	\frac{1}{6})\	\frac{1}{6})\	NOUN
bracis-33554	226	27	)	)	PUNCT
bracis-33554	226	28	.	.	PUNCT
bracis-33554	227	1	considering	consider	VERB
bracis-33554	227	2	a	a	DET
bracis-33554	227	3	confidence	confidence	NOUN
bracis-33554	227	4	level	level	NOUN
bracis-33554	227	5	of	of	ADP
bracis-33554	227	6	\(20\%\	\(20\%\	NUM
bracis-33554	227	7	)	)	PUNCT
bracis-33554	227	8	,	,	PUNCT
bracis-33554	227	9	\(v^{\pi	\(v^{\pi	VERB
bracis-33554	227	10	_	_	PUNCT
bracis-33554	227	11	2,h=1}_{\text	2,h=1}_{\text	PROPN
bracis-33554	227	12	{	{	PUNCT
bracis-33554	227	13	var}_{0.2}}=0\	var}_{0.2}}=0\	NOUN
bracis-33554	227	14	)	)	PUNCT
bracis-33554	227	15	and	and	CCONJ
bracis-33554	227	16	\(v^{\pi	\(v^{\pi	VERB
bracis-33554	227	17	_	_	NOUN
bracis-33554	227	18	2,h=1	2,h=1	NUM
bracis-33554	227	19	}	}	PUNCT
bracis-33554	228	1	_	_	PUNCT
bracis-33554	228	2	{	{	PUNCT
bracis-33554	228	3	\text	\text	INTJ
bracis-33554	228	4	{	{	PUNCT
bracis-33554	228	5	cvar}_{0.2}}=\frac{0.2	cvar}_{0.2}}=\frac{0.2	NOUN
bracis-33554	228	6	*	*	NOUN
bracis-33554	228	7	0}{0.2}=0\	0}{0.2}=0\	NUM
bracis-33554	228	8	)	)	PUNCT
bracis-33554	228	9	.	.	PUNCT
bracis-33554	229	1	thus	thus	ADV
bracis-33554	229	2	,	,	PUNCT
bracis-33554	229	3	\(g^{\pi	\(g^{\pi	PROPN
bracis-33554	229	4	_	_	NOUN
bracis-33554	229	5	2,h=1}_{\text	2,h=1}_{\text	PROPN
bracis-33554	229	6	{	{	PUNCT
bracis-33554	229	7	cvar}_{0.2	cvar}_{0.2	NOUN
bracis-33554	229	8	}	}	PUNCT
bracis-33554	229	9	}	}	PUNCT
bracis-33554	229	10	=	=	PUNCT
bracis-33554	229	11	\frac{v^{\pi	\frac{v^{\pi	VERB
bracis-33554	229	12	_	_	PUNCT
bracis-33554	229	13	2,h=1}_{\text	2,h=1}_{\text	PROPN
bracis-33554	229	14	{	{	PUNCT
bracis-33554	229	15	cvar}_{0.2	cvar}_{0.2	NOUN
bracis-33554	229	16	}	}	PUNCT
bracis-33554	229	17	}	}	PUNCT
bracis-33554	229	18	}	}	PUNCT
bracis-33554	229	19	{	{	PUNCT
bracis-33554	229	20	1	1	NUM
bracis-33554	229	21	}	}	PUNCT
bracis-33554	229	22	=	=	SYM
bracis-33554	229	23	0\	0\	PROPN
bracis-33554	229	24	)	)	PUNCT
bracis-33554	229	25	.	.	PUNCT
bracis-33554	230	1	for	for	ADP
bracis-33554	230	2	policy	policy	NOUN
bracis-33554	230	3	\(\pi	\(\pi	ADP
bracis-33554	230	4	_	_	PUNCT
bracis-33554	230	5	3\	3\	NUM
bracis-33554	230	6	)	)	PUNCT
bracis-33554	230	7	,	,	PUNCT
bracis-33554	230	8	the	the	DET
bracis-33554	230	9	only	only	ADV
bracis-33554	230	10	accumulated	accumulate	VERB
bracis-33554	230	11	reward	reward	NOUN
bracis-33554	230	12	is	be	AUX
bracis-33554	230	13	\(v_{n}^{\pi	\(v_{n}^{\pi	VERB
bracis-33554	230	14	_	_	NOUN
bracis-33554	230	15	3,h=1	3,h=1	NUM
bracis-33554	230	16	}	}	PUNCT
bracis-33554	230	17	=	=	SYM
bracis-33554	230	18	(	(	PUNCT
bracis-33554	230	19	\frac{1}{6})\	\frac{1}{6})\	PROPN
bracis-33554	230	20	)	)	PUNCT
bracis-33554	230	21	with	with	ADP
bracis-33554	230	22	distribution	distribution	NOUN
bracis-33554	230	23	\(f_{v_{n}^	\(f_{v_{n}^	ADV
bracis-33554	230	24	{	{	PUNCT
bracis-33554	230	25	\pi	\pi	ADP
bracis-33554	230	26	_	_	PROPN
bracis-33554	230	27	3}}^{h=1}=(1)\	3}}^{h=1}=(1)\	NUM
bracis-33554	230	28	)	)	PUNCT
bracis-33554	230	29	.	.	PUNCT
bracis-33554	231	1	considering	consider	VERB
bracis-33554	231	2	a	a	DET
bracis-33554	231	3	confidence	confidence	NOUN
bracis-33554	231	4	level	level	NOUN
bracis-33554	231	5	of	of	ADP
bracis-33554	231	6	\(20\%\	\(20\%\	NUM
bracis-33554	231	7	)	)	PUNCT
bracis-33554	231	8	,	,	PUNCT
bracis-33554	231	9	the	the	DET
bracis-33554	231	10	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	231	11	_	_	PUNCT
bracis-33554	231	12	3,h=1}_{\text	3,h=1}_{\text	PROPN
bracis-33554	231	13	{	{	PUNCT
bracis-33554	231	14	var}_{0.2}}=v^{\pi	var}_{0.2}}=v^{\pi	NOUN
bracis-33554	231	15	_	_	PUNCT
bracis-33554	231	16	3,h=1}_{\text	3,h=1}_{\text	NOUN
bracis-33554	231	17	{	{	PUNCT
bracis-33554	231	18	cvar}_{0.2}}=\frac{1}{6}\	cvar}_{0.2}}=\frac{1}{6}\	NOUN
bracis-33554	231	19	)	)	PUNCT
bracis-33554	231	20	,	,	PUNCT
bracis-33554	231	21	and	and	CCONJ
bracis-33554	231	22	\(g^{\pi	\(g^{\pi	X
bracis-33554	231	23	_	_	NOUN
bracis-33554	231	24	3,h=1}_{\text	3,h=1}_{\text	PROPN
bracis-33554	231	25	{	{	PUNCT
bracis-33554	231	26	cvar}_{0.2	cvar}_{0.2	NOUN
bracis-33554	231	27	}	}	PUNCT
bracis-33554	231	28	}	}	PUNCT
bracis-33554	231	29	=	=	SYM
bracis-33554	231	30	\frac{v^	\frac{v^	PROPN
bracis-33554	231	31	{	{	PUNCT
bracis-33554	231	32	\pi	\pi	PROPN
bracis-33554	231	33	_	_	PROPN
bracis-33554	231	34	3,h=1}_{\text	3,h=1}_{\text	PROPN
bracis-33554	231	35	{	{	PUNCT
bracis-33554	231	36	cvar}_{0.2}}}{1	cvar}_{0.2}}}{1	X
bracis-33554	231	37	}	}	PUNCT
bracis-33554	231	38	=	=	SYM
bracis-33554	231	39	\frac{1}{6}\	\frac{1}{6}\	NUM
bracis-33554	231	40	)	)	PUNCT
bracis-33554	231	41	.	.	PUNCT
bracis-33554	232	1	figure	figure	NOUN
bracis-33554	232	2	 	 	SPACE
bracis-33554	232	3	2a	2a	NUM
bracis-33554	232	4	)	)	PUNCT
bracis-33554	232	5	shows	show	VERB
bracis-33554	232	6	the	the	DET
bracis-33554	232	7	values	value	NOUN
bracis-33554	232	8	\(v^{\pi	\(v^{\pi	NOUN
bracis-33554	232	9	,	,	PUNCT
bracis-33554	232	10	h=1}_{\text	h=1}_{\text	PROPN
bracis-33554	232	11	{	{	PUNCT
bracis-33554	232	12	cvar}_{0.2}}\	cvar}_{0.2}}\	PROPN
bracis-33554	232	13	)	)	PUNCT
bracis-33554	232	14	for	for	ADP
bracis-33554	232	15	the	the	DET
bracis-33554	232	16	three	three	NUM
bracis-33554	232	17	policies	policy	NOUN
bracis-33554	232	18	(	(	PUNCT
bracis-33554	232	19	pink	pink	ADJ
bracis-33554	232	20	vertical	vertical	ADJ
bracis-33554	232	21	lines	line	NOUN
bracis-33554	232	22	)	)	PUNCT
bracis-33554	232	23	that	that	PRON
bracis-33554	232	24	are	be	AUX
bracis-33554	232	25	used	use	VERB
bracis-33554	232	26	to	to	PART
bracis-33554	232	27	calculate	calculate	VERB
bracis-33554	232	28	their	their	PRON
bracis-33554	232	29	respective	respective	ADJ
bracis-33554	232	30	gains	gain	NOUN
bracis-33554	232	31	.	.	PUNCT
bracis-33554	233	1	for	for	ADP
bracis-33554	233	2	\(h=1\	\(h=1\	PROPN
bracis-33554	233	3	)	)	PUNCT
bracis-33554	233	4	and	and	CCONJ
bracis-33554	233	5	a	a	DET
bracis-33554	233	6	confidence	confidence	NOUN
bracis-33554	233	7	level	level	NOUN
bracis-33554	233	8	of	of	ADP
bracis-33554	233	9	\(20\%\	\(20\%\	NUM
bracis-33554	233	10	)	)	PUNCT
bracis-33554	233	11	\(\pi	\(\pi	PROPN
bracis-33554	234	1	_	_	NOUN
bracis-33554	234	2	3	3	NUM
bracis-33554	234	3	\succ	\succ	PROPN
bracis-33554	234	4	\pi	\pi	PROPN
bracis-33554	234	5	_	_	PROPN
bracis-33554	234	6	2	2	NUM
bracis-33554	234	7	\succ	\succ	PROPN
bracis-33554	234	8	\pi	\pi	PROPN
bracis-33554	234	9	_	_	NOUN
bracis-33554	234	10	1\	1\	NUM
bracis-33554	234	11	)	)	PUNCT
bracis-33554	234	12	.	.	PUNCT
bracis-33554	235	1	the	the	DET
bracis-33554	235	2	values	value	NOUN
bracis-33554	235	3	found	find	VERB
bracis-33554	235	4	in	in	ADP
bracis-33554	235	5	this	this	DET
bracis-33554	235	6	example	example	NOUN
bracis-33554	235	7	for	for	ADP
bracis-33554	235	8	\(h=1\	\(h=1\	PROPN
bracis-33554	235	9	)	)	PUNCT
bracis-33554	235	10	are	be	AUX
bracis-33554	235	11	the	the	DET
bracis-33554	235	12	same	same	ADJ
bracis-33554	235	13	values	value	NOUN
bracis-33554	235	14	found	find	VERB
bracis-33554	235	15	with	with	ADP
bracis-33554	235	16	the	the	DET
bracis-33554	235	17	criterion	criterion	NOUN
bracis-33554	235	18	used	use	VERB
bracis-33554	235	19	by	by	ADP
bracis-33554	235	20	xia	xia	PROPN
bracis-33554	235	21	and	and	CCONJ
bracis-33554	235	22	glynn	glynn	PROPN
bracis-33554	236	1	[	[	X
bracis-33554	236	2	7	7	NUM
bracis-33554	236	3	]	]	PUNCT
bracis-33554	236	4	.	.	PUNCT
bracis-33554	237	1	4.5	4.5	NUM
bracis-33554	237	2	comparison	comparison	NOUN
bracis-33554	237	3	of	of	ADP
bracis-33554	237	4	\(g^{\pi	\(g^{\pi	NOUN
bracis-33554	237	5	}	}	PUNCT
bracis-33554	237	6	\	\	PROPN
bracis-33554	237	7	)	)	PUNCT
bracis-33554	237	8	,	,	PUNCT
bracis-33554	237	9	\(g_{u}^{\pi	\(g_{u}^{\pi	NOUN
bracis-33554	237	10	,	,	PUNCT
bracis-33554	237	11	h}\	h}\	PROPN
bracis-33554	237	12	)	)	PUNCT
bracis-33554	237	13	,	,	PUNCT
bracis-33554	237	14	\(g_{\text	\(g_{\text	NOUN
bracis-33554	237	15	{	{	PUNCT
bracis-33554	237	16	var}}^{\pi	var}}^{\pi	ADJ
bracis-33554	237	17	,	,	PUNCT
bracis-33554	237	18	h}\	h}\	NUM
bracis-33554	237	19	)	)	PUNCT
bracis-33554	237	20	and	and	CCONJ
bracis-33554	237	21	\(g_{\text	\(g_{\text	NOUN
bracis-33554	237	22	{	{	PUNCT
bracis-33554	237	23	cvar}}^{\pi	cvar}}^{\pi	NOUN
bracis-33554	237	24	,	,	PUNCT
bracis-33554	237	25	h}\	h}\	NUM
bracis-33554	237	26	)	)	PUNCT
bracis-33554	237	27	figure	figure	NOUN
bracis-33554	237	28	 	 	SPACE
bracis-33554	237	29	3a	3a	NUM
bracis-33554	237	30	)	)	PUNCT
bracis-33554	237	31	shows	show	VERB
bracis-33554	237	32	(	(	PUNCT
bracis-33554	237	33	\(g_{u}^{\pi	\(g_{u}^{\pi	NOUN
bracis-33554	237	34	,	,	PUNCT
bracis-33554	237	35	h}\	h}\	PROPN
bracis-33554	237	36	)	)	PUNCT
bracis-33554	237	37	)	)	PUNCT
bracis-33554	237	38	for	for	ADP
bracis-33554	237	39	\(1	\(1	PROPN
bracis-33554	237	40	\le	\le	PROPN
bracis-33554	237	41	h	h	PROPN
bracis-33554	237	42	\le	\le	PROPN
bracis-33554	237	43	2000\	2000\	NUM
bracis-33554	237	44	)	)	PUNCT
bracis-33554	237	45	and	and	CCONJ
bracis-33554	237	46	for	for	ADP
bracis-33554	237	47	risk	risk	NOUN
bracis-33554	237	48	factors	factor	NOUN
bracis-33554	237	49	\(\gamma	\(\gamma	VERB
bracis-33554	237	50	\in	\in	X
bracis-33554	237	51	\{1	\{1	NOUN
bracis-33554	237	52	,	,	PUNCT
bracis-33554	237	53	0.1	0.1	NUM
bracis-33554	237	54	,	,	PUNCT
bracis-33554	237	55	0.01	0.01	NUM
bracis-33554	237	56	,	,	PUNCT
bracis-33554	237	57	0.001\}\	0.001\}\	NUM
bracis-33554	237	58	)	)	PUNCT
bracis-33554	237	59	.	.	PUNCT
bracis-33554	238	1	for	for	ADP
bracis-33554	238	2	all	all	DET
bracis-33554	238	3	policies	policy	NOUN
bracis-33554	238	4	,	,	PUNCT
bracis-33554	238	5	it	it	PRON
bracis-33554	238	6	is	be	AUX
bracis-33554	238	7	noted	note	VERB
bracis-33554	238	8	that	that	SCONJ
bracis-33554	238	9	when	when	SCONJ
bracis-33554	238	10	\(\gamma	\(\gamma	ADP
bracis-33554	238	11	\	\	NOUN
bracis-33554	238	12	)	)	PUNCT
bracis-33554	238	13	tends	tend	VERB
bracis-33554	238	14	to	to	ADP
bracis-33554	238	15	0	0	NUM
bracis-33554	238	16	for	for	ADP
bracis-33554	238	17	any	any	DET
bracis-33554	238	18	value	value	NOUN
bracis-33554	238	19	of	of	ADP
bracis-33554	238	20	h	h	NOUN
bracis-33554	238	21	the	the	DET
bracis-33554	238	22	value	value	NOUN
bracis-33554	238	23	of	of	ADP
bracis-33554	238	24	the	the	DET
bracis-33554	238	25	utility	utility	NOUN
bracis-33554	238	26	function	function	NOUN
bracis-33554	238	27	\(g_{u_\gamma	\(g_{u_\gamma	PROPN
bracis-33554	238	28	}	}	PUNCT
bracis-33554	238	29	^{\pi	^{\pi	NUM
bracis-33554	238	30	,	,	PUNCT
bracis-33554	238	31	h}\	h}\	NUM
bracis-33554	238	32	)	)	PUNCT
bracis-33554	238	33	tends	tend	VERB
bracis-33554	238	34	to	to	ADP
bracis-33554	238	35	the	the	DET
bracis-33554	238	36	risk	risk	NOUN
bracis-33554	238	37	-	-	PUNCT
bracis-33554	238	38	neutral	neutral	ADJ
bracis-33554	238	39	gain	gain	NOUN
bracis-33554	238	40	,	,	PUNCT
bracis-33554	238	41	\(g^{\pi	\(g^{\pi	ADJ
bracis-33554	238	42	}	}	PUNCT
bracis-33554	238	43	\	\	NOUN
bracis-33554	238	44	)	)	PUNCT
bracis-33554	238	45	.	.	PUNCT
bracis-33554	239	1	this	this	DET
bracis-33554	239	2	property	property	NOUN
bracis-33554	239	3	was	be	AUX
bracis-33554	239	4	demonstrated	demonstrate	VERB
bracis-33554	239	5	by	by	ADP
bracis-33554	239	6	howard	howard	PROPN
bracis-33554	239	7	and	and	CCONJ
bracis-33554	239	8	matheson	matheson	PROPN
bracis-33554	240	1	[	[	X
bracis-33554	240	2	2	2	NUM
bracis-33554	240	3	]	]	PUNCT
bracis-33554	240	4	for	for	ADP
bracis-33554	240	5	\(h=\infty	\(h=\infty	ADJ
bracis-33554	240	6	\	\	NOUN
bracis-33554	240	7	)	)	PUNCT
bracis-33554	240	8	.	.	PUNCT
bracis-33554	241	1	it	it	PRON
bracis-33554	241	2	is	be	AUX
bracis-33554	241	3	also	also	ADV
bracis-33554	241	4	observed	observe	VERB
bracis-33554	241	5	that	that	SCONJ
bracis-33554	241	6	for	for	ADP
bracis-33554	241	7	all	all	DET
bracis-33554	241	8	policies	policy	NOUN
bracis-33554	241	9	,	,	PUNCT
bracis-33554	241	10	the	the	DET
bracis-33554	241	11	gain	gain	NOUN
bracis-33554	241	12	\(g_{u_1}^{\pi	\(g_{u_1}^{\pi	X
bracis-33554	241	13	,	,	PUNCT
bracis-33554	241	14	h}\	h}\	PROPN
bracis-33554	241	15	)	)	PUNCT
bracis-33554	241	16	when	when	SCONJ
bracis-33554	241	17	h	h	NOUN
bracis-33554	241	18	tends	tend	VERB
bracis-33554	241	19	to	to	PART
bracis-33554	241	20	infinity	infinity	VERB
bracis-33554	241	21	approaches	approach	NOUN
bracis-33554	241	22	\(g_{u_1}^{\pi	\(g_{u_1}^{\pi	PROPN
bracis-33554	241	23	,	,	PUNCT
bracis-33554	241	24	h=\infty	h=\infty	ADJ
bracis-33554	241	25	}	}	PUNCT
bracis-33554	241	26	\	\	NOUN
bracis-33554	241	27	)	)	PUNCT
bracis-33554	241	28	.	.	PUNCT
bracis-33554	242	1	additionally	additionally	ADV
bracis-33554	242	2	,	,	PUNCT
bracis-33554	242	3	if	if	SCONJ
bracis-33554	242	4	\(h=\infty	\(h=\infty	ADJ
bracis-33554	242	5	\	\	NOUN
bracis-33554	242	6	)	)	PUNCT
bracis-33554	242	7	(	(	PUNCT
bracis-33554	242	8	orange	orange	NOUN
bracis-33554	242	9	lines	line	NOUN
bracis-33554	242	10	in	in	ADP
bracis-33554	242	11	fig	fig	NOUN
bracis-33554	242	12	.	.	PUNCT
bracis-33554	242	13	 	 	SPACE
bracis-33554	242	14	3	3	NUM
bracis-33554	242	15	)	)	PUNCT
bracis-33554	242	16	,	,	PUNCT
bracis-33554	242	17	\(\pi	\(\pi	PROPN
bracis-33554	243	1	_	_	NOUN
bracis-33554	243	2	3	3	NUM
bracis-33554	243	3	\succ	\succ	PROPN
bracis-33554	243	4	\pi	\pi	PROPN
bracis-33554	243	5	_	_	PROPN
bracis-33554	243	6	1	1	NUM
bracis-33554	243	7	\sim	\sim	NOUN
bracis-33554	243	8	\pi	\pi	PROPN
bracis-33554	243	9	_	_	NOUN
bracis-33554	243	10	2\	2\	NUM
bracis-33554	243	11	)	)	PUNCT
bracis-33554	243	12	and	and	CCONJ
bracis-33554	243	13	if	if	SCONJ
bracis-33554	243	14	\(h	\(h	PROPN
bracis-33554	243	15	\ne	\ne	PROPN
bracis-33554	243	16	\infty	\infty	PROPN
bracis-33554	243	17	\	\	PROPN
bracis-33554	243	18	)	)	PUNCT
bracis-33554	243	19	(	(	PUNCT
bracis-33554	243	20	dotted	dot	VERB
bracis-33554	243	21	lines	line	NOUN
bracis-33554	243	22	in	in	ADP
bracis-33554	243	23	fig	fig	NOUN
bracis-33554	243	24	.	.	PUNCT
bracis-33554	243	25	 	 	SPACE
bracis-33554	243	26	3	3	X
bracis-33554	243	27	)	)	PUNCT
bracis-33554	243	28	\(\pi	\(\pi	ADP
bracis-33554	244	1	_	_	NOUN
bracis-33554	244	2	3	3	NUM
bracis-33554	244	3	\succ	\succ	PROPN
bracis-33554	244	4	\pi	\pi	PROPN
bracis-33554	244	5	_	_	PROPN
bracis-33554	244	6	2	2	NUM
bracis-33554	244	7	\succ	\succ	PROPN
bracis-33554	244	8	\pi	\pi	PROPN
bracis-33554	244	9	_	_	NOUN
bracis-33554	244	10	1\	1\	NUM
bracis-33554	244	11	)	)	PUNCT
bracis-33554	244	12	.	.	PUNCT
bracis-33554	245	1	fig	fig	NOUN
bracis-33554	245	2	.	.	PUNCT
bracis-33554	246	1	3	3	X
bracis-33554	246	2	.	.	X
bracis-33554	246	3	gain	gain	NOUN
bracis-33554	246	4	of	of	ADP
bracis-33554	246	5	the	the	DET
bracis-33554	246	6	policies	policy	NOUN
bracis-33554	246	7	varying	vary	VERB
bracis-33554	246	8	h.	h.	PROPN
bracis-33554	246	9	full	full	ADJ
bracis-33554	246	10	size	size	NOUN
bracis-33554	246	11	image	image	NOUN
bracis-33554	246	12	figure	figure	NOUN
bracis-33554	246	13	 	 	SPACE
bracis-33554	246	14	3b	3b	NUM
bracis-33554	246	15	)	)	PUNCT
bracis-33554	246	16	shows	show	VERB
bracis-33554	246	17	\(g_{\text	\(g_{\text	NOUN
bracis-33554	246	18	{	{	PUNCT
bracis-33554	246	19	var}}^{\pi	var}}^{\pi	ADJ
bracis-33554	246	20	,	,	PUNCT
bracis-33554	246	21	h}\	h}\	NUM
bracis-33554	246	22	)	)	PUNCT
bracis-33554	246	23	for	for	ADP
bracis-33554	246	24	\(1	\(1	PROPN
bracis-33554	246	25	\le	\le	PROPN
bracis-33554	246	26	h	h	PROPN
bracis-33554	246	27	\le	\le	PROPN
bracis-33554	246	28	2000\	2000\	NUM
bracis-33554	246	29	)	)	PUNCT
bracis-33554	246	30	and	and	CCONJ
bracis-33554	246	31	for	for	ADP
bracis-33554	246	32	confidence	confidence	NOUN
bracis-33554	246	33	levels	level	NOUN
bracis-33554	246	34	\(\alpha	\(\alpha	VERB
bracis-33554	246	35	\in	\in	PROPN
bracis-33554	246	36	\{0.01	\{0.01	PROPN
bracis-33554	246	37	,	,	PUNCT
bracis-33554	246	38	0.1	0.1	NUM
bracis-33554	246	39	,	,	PUNCT
bracis-33554	246	40	0.2	0.2	NUM
bracis-33554	246	41	,	,	PUNCT
bracis-33554	246	42	0.5,0.8,0.9,0.99\}\	0.5,0.8,0.9,0.99\}\	NUM
bracis-33554	246	43	)	)	PUNCT
bracis-33554	246	44	.	.	PUNCT
bracis-33554	247	1	for	for	ADP
bracis-33554	247	2	policies	policy	NOUN
bracis-33554	247	3	\(\pi	\(\pi	ADP
bracis-33554	247	4	_	_	PRON
bracis-33554	247	5	1\	1\	NUM
bracis-33554	247	6	)	)	PUNCT
bracis-33554	247	7	and	and	CCONJ
bracis-33554	247	8	\(\pi	\(\pi	ADP
bracis-33554	247	9	_	_	NOUN
bracis-33554	247	10	2\	2\	X
bracis-33554	247	11	)	)	PUNCT
bracis-33554	247	12	,	,	PUNCT
bracis-33554	247	13	for	for	ADP
bracis-33554	247	14	confidence	confidence	NOUN
bracis-33554	247	15	levels	level	NOUN
bracis-33554	247	16	above	above	ADP
bracis-33554	247	17	\(50\%\	\(50\%\	PRON
bracis-33554	247	18	)	)	PUNCT
bracis-33554	247	19	,	,	PUNCT
bracis-33554	247	20	\(g_{\text	\(g_{\text	NOUN
bracis-33554	247	21	{	{	PUNCT
bracis-33554	247	22	var}_\alpha	var}_\alpha	NOUN
bracis-33554	247	23	}	}	PUNCT
bracis-33554	247	24	^{\pi	^{\pi	NUM
bracis-33554	247	25	,	,	PUNCT
bracis-33554	247	26	h	h	NOUN
bracis-33554	247	27	}	}	PUNCT
bracis-33554	247	28	\ge	\ge	PROPN
bracis-33554	247	29	g^\pi	g^\pi	NOUN
bracis-33554	247	30	\	\	NOUN
bracis-33554	247	31	)	)	PUNCT
bracis-33554	247	32	if	if	SCONJ
bracis-33554	247	33	\(h	\(h	PROPN
bracis-33554	247	34	\ge	\ge	PROPN
bracis-33554	247	35	1\	1\	NUM
bracis-33554	247	36	)	)	PUNCT
bracis-33554	247	37	.	.	PUNCT
bracis-33554	248	1	when	when	SCONJ
bracis-33554	248	2	h	h	NOUN
bracis-33554	248	3	tends	tend	VERB
bracis-33554	248	4	to	to	PART
bracis-33554	248	5	infinity	infinity	VERB
bracis-33554	248	6	\(g_{\text	\(g_{\text	NOUN
bracis-33554	248	7	{	{	PUNCT
bracis-33554	248	8	var}_\alpha	var}_\alpha	NOUN
bracis-33554	248	9	}	}	PUNCT
bracis-33554	248	10	^{\pi	^{\pi	NUM
bracis-33554	248	11	,	,	PUNCT
bracis-33554	248	12	h}\	h}\	NUM
bracis-33554	248	13	)	)	PUNCT
bracis-33554	248	14	tends	tend	VERB
bracis-33554	248	15	to	to	PART
bracis-33554	248	16	\(g^\pi	\(g^\pi	VERB
bracis-33554	248	17	\	\	NOUN
bracis-33554	248	18	)	)	PUNCT
bracis-33554	248	19	.	.	PUNCT
bracis-33554	249	1	for	for	ADP
bracis-33554	249	2	confidence	confidence	NOUN
bracis-33554	249	3	levels	level	NOUN
bracis-33554	249	4	below	below	ADP
bracis-33554	249	5	\(50\%\	\(50\%\	PRON
bracis-33554	249	6	)	)	PUNCT
bracis-33554	249	7	,	,	PUNCT
bracis-33554	249	8	\(g_{\text	\(g_{\text	NOUN
bracis-33554	249	9	{	{	PUNCT
bracis-33554	249	10	var}_\alpha	var}_\alpha	NOUN
bracis-33554	249	11	}	}	PUNCT
bracis-33554	249	12	^{\pi	^{\pi	NUM
bracis-33554	249	13	,	,	PUNCT
bracis-33554	249	14	h	h	NOUN
bracis-33554	249	15	}	}	PUNCT
bracis-33554	249	16	\le	\le	PROPN
bracis-33554	249	17	g^\pi	g^\pi	NOUN
bracis-33554	249	18	\	\	NOUN
bracis-33554	249	19	)	)	PUNCT
bracis-33554	250	1	if	if	SCONJ
bracis-33554	250	2	\(h	\(h	PROPN
bracis-33554	250	3	\ge	\ge	PROPN
bracis-33554	250	4	2\	2\	NUM
bracis-33554	250	5	)	)	PUNCT
bracis-33554	250	6	and	and	CCONJ
bracis-33554	250	7	approaches	approach	VERB
bracis-33554	250	8	\	\	PROPN
bracis-33554	250	9	(	(	PUNCT
bracis-33554	250	10	g^\pi	g^\pi	PROPN
bracis-33554	250	11	\	\	NOUN
bracis-33554	250	12	)	)	PUNCT
bracis-33554	250	13	when	when	SCONJ
bracis-33554	250	14	h	h	NOUN
bracis-33554	250	15	tends	tend	VERB
bracis-33554	250	16	to	to	PART
bracis-33554	250	17	infinity	infinity	VERB
bracis-33554	250	18	.	.	PUNCT
bracis-33554	251	1	for	for	ADP
bracis-33554	251	2	policy	policy	NOUN
bracis-33554	251	3	\(\pi	\(\pi	ADP
bracis-33554	251	4	_	_	PUNCT
bracis-33554	251	5	3\	3\	NUM
bracis-33554	251	6	)	)	PUNCT
bracis-33554	251	7	,	,	PUNCT
bracis-33554	251	8	\(g_{\text	\(g_{\text	NOUN
bracis-33554	251	9	{	{	PUNCT
bracis-33554	251	10	var}_\alpha	var}_\alpha	NOUN
bracis-33554	251	11	}	}	PUNCT
bracis-33554	251	12	^{\pi	^{\pi	NUM
bracis-33554	251	13	,	,	PUNCT
bracis-33554	251	14	h}=g^\pi	h}=g^\pi	PROPN
bracis-33554	251	15	\	\	NOUN
bracis-33554	251	16	)	)	PUNCT
bracis-33554	251	17	for	for	ADP
bracis-33554	251	18	all	all	DET
bracis-33554	251	19	h.	h.	PROPN
bracis-33554	251	20	figure	figure	PROPN
bracis-33554	251	21	 	 	SPACE
bracis-33554	251	22	3c	3c	NUM
bracis-33554	251	23	)	)	PUNCT
bracis-33554	251	24	shows	show	VERB
bracis-33554	251	25	\(g_{\text	\(g_{\text	NOUN
bracis-33554	251	26	{	{	PUNCT
bracis-33554	251	27	cvar}}^{\pi	cvar}}^{\pi	NOUN
bracis-33554	251	28	,	,	PUNCT
bracis-33554	251	29	h}\	h}\	PROPN
bracis-33554	251	30	)	)	PUNCT
bracis-33554	251	31	for	for	ADP
bracis-33554	251	32	\(1	\(1	PROPN
bracis-33554	251	33	\le	\le	PROPN
bracis-33554	251	34	h	h	PROPN
bracis-33554	251	35	\le	\le	PROPN
bracis-33554	251	36	2000\	2000\	NUM
bracis-33554	251	37	)	)	PUNCT
bracis-33554	251	38	and	and	CCONJ
bracis-33554	251	39	for	for	ADP
bracis-33554	251	40	confidence	confidence	NOUN
bracis-33554	251	41	levels	level	NOUN
bracis-33554	251	42	\(\alpha	\(\alpha	VERB
bracis-33554	251	43	\in	\in	PROPN
bracis-33554	251	44	\{0.01	\{0.01	PROPN
bracis-33554	251	45	,	,	PUNCT
bracis-33554	251	46	0.1	0.1	NUM
bracis-33554	251	47	,	,	PUNCT
bracis-33554	251	48	0.2	0.2	NUM
bracis-33554	251	49	,	,	PUNCT
bracis-33554	251	50	0.5,0.8,0.9,0.99\}\	0.5,0.8,0.9,0.99\}\	NUM
bracis-33554	251	51	)	)	PUNCT
bracis-33554	251	52	.	.	PUNCT
bracis-33554	252	1	the	the	DET
bracis-33554	252	2	values	value	NOUN
bracis-33554	252	3	\(g_{\text	\(g_{\text	VERB
bracis-33554	252	4	{	{	PUNCT
bracis-33554	252	5	cvar}_\alpha	cvar}_\alpha	NOUN
bracis-33554	252	6	}	}	PUNCT
bracis-33554	252	7	^{\pi	^{\pi	NUM
bracis-33554	252	8	,	,	PUNCT
bracis-33554	252	9	h}\	h}\	NUM
bracis-33554	252	10	)	)	PUNCT
bracis-33554	252	11	tend	tend	VERB
bracis-33554	252	12	to	to	PART
bracis-33554	252	13	\(g^\pi	\(g^\pi	VERB
bracis-33554	252	14	\	\	NOUN
bracis-33554	252	15	)	)	PUNCT
bracis-33554	252	16	when	when	SCONJ
bracis-33554	252	17	h	h	NOUN
bracis-33554	252	18	tends	tend	VERB
bracis-33554	252	19	to	to	PART
bracis-33554	252	20	infinity	infinity	VERB
bracis-33554	252	21	for	for	ADP
bracis-33554	252	22	any	any	DET
bracis-33554	252	23	value	value	NOUN
bracis-33554	252	24	of	of	ADP
bracis-33554	252	25	\(\alpha	\(\alpha	NOUN
bracis-33554	252	26	\	\	NOUN
bracis-33554	252	27	)	)	PUNCT
bracis-33554	252	28	and	and	CCONJ
bracis-33554	252	29	,	,	PUNCT
bracis-33554	252	30	as	as	SCONJ
bracis-33554	252	31	expected	expect	VERB
bracis-33554	252	32	,	,	PUNCT
bracis-33554	252	33	when	when	SCONJ
bracis-33554	252	34	\(\alpha	\(\alpha	ADV
bracis-33554	252	35	\	\	NOUN
bracis-33554	252	36	)	)	PUNCT
bracis-33554	252	37	tends	tend	VERB
bracis-33554	252	38	to	to	ADP
bracis-33554	252	39	1	1	NUM
bracis-33554	252	40	,	,	PUNCT
bracis-33554	252	41	\(g_{\text	\(g_{\text	NOUN
bracis-33554	252	42	{	{	PUNCT
bracis-33554	252	43	cvar}_\alpha	cvar}_\alpha	NOUN
bracis-33554	252	44	}	}	PUNCT
bracis-33554	252	45	^{\pi	^{\pi	NUM
bracis-33554	252	46	,	,	PUNCT
bracis-33554	252	47	h}\	h}\	NUM
bracis-33554	252	48	)	)	PUNCT
bracis-33554	252	49	approaches	approach	VERB
bracis-33554	252	50	\(g^\pi	\(g^\pi	PUNCT
bracis-33554	252	51	\	\	NOUN
bracis-33554	252	52	)	)	PUNCT
bracis-33554	252	53	for	for	ADP
bracis-33554	252	54	any	any	DET
bracis-33554	252	55	h.	h.	NOUN
bracis-33554	252	56	additionally	additionally	ADV
bracis-33554	252	57	,	,	PUNCT
bracis-33554	252	58	if	if	SCONJ
bracis-33554	252	59	\(h=\infty	\(h=\infty	ADJ
bracis-33554	252	60	\	\	NOUN
bracis-33554	252	61	)	)	PUNCT
bracis-33554	252	62	,	,	PUNCT
bracis-33554	253	1	\(\pi	\(\pi	PROPN
bracis-33554	253	2	_	_	PRON
bracis-33554	253	3	1	1	NUM
bracis-33554	253	4	\sim	\sim	NOUN
bracis-33554	253	5	\pi	\pi	PROPN
bracis-33554	253	6	_	_	PROPN
bracis-33554	253	7	2	2	NUM
bracis-33554	253	8	\sim	\sim	NOUN
bracis-33554	253	9	\pi	\pi	ADP
bracis-33554	253	10	_	_	NOUN
bracis-33554	253	11	3\	3\	NUM
bracis-33554	253	12	)	)	PUNCT
bracis-33554	253	13	and	and	CCONJ
bracis-33554	253	14	if	if	SCONJ
bracis-33554	253	15	\(h	\(h	PROPN
bracis-33554	253	16	\ne	\ne	PROPN
bracis-33554	253	17	\infty	\infty	PROPN
bracis-33554	253	18	\	\	PROPN
bracis-33554	253	19	)	)	PUNCT
bracis-33554	253	20	(	(	PUNCT
bracis-33554	253	21	dotted	dot	VERB
bracis-33554	253	22	lines	line	NOUN
bracis-33554	253	23	in	in	ADP
bracis-33554	253	24	fig	fig	NOUN
bracis-33554	253	25	.	.	PUNCT
bracis-33554	253	26	 	 	SPACE
bracis-33554	254	1	3	3	X
bracis-33554	254	2	)	)	PUNCT
bracis-33554	255	1	\(\pi	\(\pi	ADP
bracis-33554	256	1	_	_	NOUN
bracis-33554	256	2	3	3	NUM
bracis-33554	256	3	\succeq	\succeq	PROPN
bracis-33554	256	4	\pi	\pi	NOUN
bracis-33554	256	5	_	_	NOUN
bracis-33554	256	6	2	2	NUM
bracis-33554	256	7	\succeq	\succeq	PROPN
bracis-33554	256	8	\pi	\pi	NOUN
bracis-33554	256	9	_	_	NOUN
bracis-33554	256	10	1\	1\	NUM
bracis-33554	256	11	)	)	PUNCT
bracis-33554	256	12	.	.	PUNCT
bracis-33554	257	1	5	5	NUM
bracis-33554	257	2	conclusions	conclusion	NOUN
bracis-33554	257	3	in	in	ADP
bracis-33554	257	4	this	this	DET
bracis-33554	257	5	work	work	NOUN
bracis-33554	257	6	,	,	PUNCT
bracis-33554	257	7	we	we	PRON
bracis-33554	257	8	proposed	propose	VERB
bracis-33554	257	9	a	a	DET
bracis-33554	257	10	mathematical	mathematical	ADJ
bracis-33554	257	11	framework	framework	NOUN
bracis-33554	257	12	that	that	PRON
bracis-33554	257	13	unifies	unify	VERB
bracis-33554	257	14	the	the	DET
bracis-33554	257	15	average	average	ADJ
bracis-33554	257	16	reward	reward	NOUN
bracis-33554	257	17	and	and	CCONJ
bracis-33554	257	18	risk	risk	NOUN
bracis-33554	257	19	criteria	criterion	NOUN
bracis-33554	257	20	for	for	ADP
bracis-33554	257	21	mdps	mdps	NOUN
bracis-33554	257	22	,	,	PUNCT
bracis-33554	257	23	for	for	ADP
bracis-33554	257	24	stationary	stationary	ADJ
bracis-33554	257	25	policies	policy	NOUN
bracis-33554	257	26	that	that	PRON
bracis-33554	257	27	generate	generate	VERB
bracis-33554	257	28	aperiodic	aperiodic	ADJ
bracis-33554	257	29	unichain	unichain	NOUN
bracis-33554	257	30	or	or	CCONJ
bracis-33554	257	31	multichain	multichain	NOUN
bracis-33554	257	32	markov	markov	NOUN
bracis-33554	257	33	chains	chain	NOUN
bracis-33554	257	34	.	.	PUNCT
bracis-33554	258	1	the	the	DET
bracis-33554	258	2	proposed	propose	VERB
bracis-33554	258	3	formalization	formalization	NOUN
bracis-33554	258	4	uses	use	VERB
bracis-33554	258	5	sequences	sequence	NOUN
bracis-33554	258	6	of	of	ADP
bracis-33554	258	7	states	state	NOUN
bracis-33554	258	8	of	of	ADP
bracis-33554	258	9	size	size	NOUN
bracis-33554	258	10	h	h	NOUN
bracis-33554	258	11	,	,	PUNCT
bracis-33554	258	12	allowing	allow	VERB
bracis-33554	258	13	two	two	NUM
bracis-33554	258	14	ways	way	NOUN
bracis-33554	258	15	of	of	ADP
bracis-33554	258	16	thinking	think	VERB
bracis-33554	258	17	about	about	ADP
bracis-33554	258	18	the	the	DET
bracis-33554	258	19	stochastic	stochastic	ADJ
bracis-33554	258	20	process	process	NOUN
bracis-33554	258	21	in	in	ADP
bracis-33554	258	22	the	the	DET
bracis-33554	258	23	limit	limit	NOUN
bracis-33554	258	24	:	:	PUNCT
bracis-33554	258	25	(	(	PUNCT
bracis-33554	258	26	i	i	NOUN
bracis-33554	258	27	)	)	PUNCT
bracis-33554	258	28	the	the	DET
bracis-33554	258	29	accumulated	accumulate	VERB
bracis-33554	258	30	reward	reward	NOUN
bracis-33554	258	31	at	at	ADP
bracis-33554	258	32	infinity	infinity	NOUN
bracis-33554	258	33	and	and	CCONJ
bracis-33554	258	34	(	(	PUNCT
bracis-33554	258	35	ii	ii	NOUN
bracis-33554	258	36	)	)	PUNCT
bracis-33554	258	37	the	the	DET
bracis-33554	258	38	steady	steady	ADJ
bracis-33554	258	39	-	-	PUNCT
bracis-33554	258	40	state	state	NOUN
bracis-33554	258	41	distribution	distribution	NOUN
bracis-33554	258	42	.	.	PUNCT
bracis-33554	259	1	the	the	DET
bracis-33554	259	2	gain	gain	NOUN
bracis-33554	259	3	from	from	ADP
bracis-33554	259	4	the	the	DET
bracis-33554	259	5	risk	risk	NOUN
bracis-33554	259	6	-	-	PUNCT
bracis-33554	259	7	neutral	neutral	ADJ
bracis-33554	259	8	average	average	ADJ
bracis-33554	259	9	reward	reward	NOUN
bracis-33554	259	10	criterion	criterion	NOUN
bracis-33554	259	11	does	do	AUX
bracis-33554	259	12	not	not	PART
bracis-33554	259	13	vary	vary	VERB
bracis-33554	259	14	regardless	regardless	ADV
bracis-33554	259	15	of	of	ADP
bracis-33554	259	16	the	the	DET
bracis-33554	259	17	number	number	NOUN
bracis-33554	259	18	of	of	ADP
bracis-33554	259	19	states	state	NOUN
bracis-33554	259	20	in	in	ADP
bracis-33554	259	21	the	the	DET
bracis-33554	259	22	sequence	sequence	NOUN
bracis-33554	259	23	.	.	PUNCT
bracis-33554	260	1	works	work	VERB
bracis-33554	260	2	on	on	ADP
bracis-33554	260	3	average	average	ADJ
bracis-33554	260	4	reward	reward	NOUN
bracis-33554	260	5	with	with	ADP
bracis-33554	260	6	exponential	exponential	ADJ
bracis-33554	260	7	utility	utility	NOUN
bracis-33554	260	8	function	function	NOUN
bracis-33554	260	9	[	[	X
bracis-33554	260	10	2	2	NUM
bracis-33554	260	11	]	]	PUNCT
bracis-33554	260	12	and	and	CCONJ
bracis-33554	260	13	with	with	ADP
bracis-33554	260	14	the	the	DET
bracis-33554	260	15	cvar	cvar	PROPN
bracis-33554	260	16	risk	risk	NOUN
bracis-33554	260	17	measure	measure	NOUN
bracis-33554	260	18	[	[	X
bracis-33554	260	19	7	7	X
bracis-33554	260	20	]	]	PUNCT
bracis-33554	260	21	have	have	AUX
bracis-33554	260	22	been	be	AUX
bracis-33554	260	23	classified	classify	VERB
bracis-33554	260	24	using	use	VERB
bracis-33554	260	25	the	the	DET
bracis-33554	260	26	proposed	propose	VERB
bracis-33554	260	27	framework	framework	NOUN
bracis-33554	260	28	.	.	PUNCT
bracis-33554	261	1	the	the	DET
bracis-33554	261	2	exponential	exponential	ADJ
bracis-33554	261	3	utility	utility	NOUN
bracis-33554	261	4	criterion	criterion	NOUN
bracis-33554	261	5	[	[	X
bracis-33554	261	6	2	2	NUM
bracis-33554	261	7	]	]	PUNCT
bracis-33554	261	8	was	be	AUX
bracis-33554	261	9	classified	classify	VERB
bracis-33554	261	10	as	as	ADP
bracis-33554	261	11	\(h=\infty	\(h=\infty	NUM
bracis-33554	261	12	\	\	NOUN
bracis-33554	261	13	)	)	PUNCT
bracis-33554	261	14	since	since	SCONJ
bracis-33554	261	15	the	the	DET
bracis-33554	261	16	sum	sum	NOUN
bracis-33554	261	17	of	of	ADP
bracis-33554	261	18	the	the	DET
bracis-33554	261	19	reward	reward	NOUN
bracis-33554	261	20	at	at	ADP
bracis-33554	261	21	infinity	infinity	NOUN
bracis-33554	261	22	was	be	AUX
bracis-33554	261	23	used	use	VERB
bracis-33554	261	24	,	,	PUNCT
bracis-33554	261	25	and	and	CCONJ
bracis-33554	262	1	the	the	DET
bracis-33554	262	2	cvar	cvar	NOUN
bracis-33554	262	3	criterion	criterion	NOUN
bracis-33554	262	4	[	[	X
bracis-33554	262	5	7	7	NUM
bracis-33554	262	6	]	]	PUNCT
bracis-33554	262	7	was	be	AUX
bracis-33554	262	8	classified	classify	VERB
bracis-33554	262	9	as	as	ADP
bracis-33554	262	10	\(h=1\	\(h=1\	PROPN
bracis-33554	262	11	)	)	PUNCT
bracis-33554	262	12	because	because	SCONJ
bracis-33554	262	13	it	it	PRON
bracis-33554	262	14	considered	consider	VERB
bracis-33554	262	15	the	the	DET
bracis-33554	262	16	immediate	immediate	ADJ
bracis-33554	262	17	reward	reward	NOUN
bracis-33554	262	18	and	and	CCONJ
bracis-33554	262	19	the	the	DET
bracis-33554	262	20	steady	steady	ADJ
bracis-33554	262	21	-	-	PUNCT
bracis-33554	262	22	state	state	NOUN
bracis-33554	262	23	distribution	distribution	NOUN
bracis-33554	262	24	.	.	PUNCT
bracis-33554	263	1	to	to	ADP
bracis-33554	263	2	the	the	DET
bracis-33554	263	3	best	good	ADJ
bracis-33554	263	4	of	of	ADP
bracis-33554	263	5	our	our	PRON
bracis-33554	263	6	knowledge	knowledge	NOUN
bracis-33554	263	7	,	,	PUNCT
bracis-33554	263	8	the	the	DET
bracis-33554	263	9	exponential	exponential	ADJ
bracis-33554	263	10	utility	utility	NOUN
bracis-33554	263	11	function	function	NOUN
bracis-33554	263	12	applied	apply	VERB
bracis-33554	263	13	to	to	ADP
bracis-33554	263	14	sequences	sequence	NOUN
bracis-33554	263	15	of	of	ADP
bracis-33554	263	16	states	state	NOUN
bracis-33554	263	17	of	of	ADP
bracis-33554	263	18	size	size	NOUN
bracis-33554	263	19	\(h=1\	\(h=1\	PROPN
bracis-33554	263	20	)	)	PUNCT
bracis-33554	263	21	does	do	AUX
bracis-33554	263	22	not	not	PART
bracis-33554	263	23	exist	exist	VERB
bracis-33554	263	24	in	in	ADP
bracis-33554	263	25	the	the	DET
bracis-33554	263	26	literature	literature	NOUN
bracis-33554	263	27	.	.	PUNCT
bracis-33554	264	1	this	this	DET
bracis-33554	264	2	criterion	criterion	NOUN
bracis-33554	264	3	allowed	allow	VERB
bracis-33554	264	4	differentiation	differentiation	NOUN
bracis-33554	264	5	of	of	ADP
bracis-33554	264	6	policies	policy	NOUN
bracis-33554	264	7	not	not	PART
bracis-33554	264	8	distinguished	distinguish	VERB
bracis-33554	264	9	by	by	ADP
bracis-33554	264	10	exponential	exponential	ADJ
bracis-33554	264	11	utility	utility	NOUN
bracis-33554	264	12	with	with	ADP
bracis-33554	264	13	\(h=\infty	\(h=\infty	PROPN
bracis-33554	264	14	\	\	NOUN
bracis-33554	264	15	)	)	PUNCT
bracis-33554	264	16	and	and	CCONJ
bracis-33554	264	17	by	by	ADP
bracis-33554	264	18	risk	risk	NOUN
bracis-33554	264	19	-	-	PUNCT
bracis-33554	264	20	neutral	neutral	ADJ
bracis-33554	264	21	average	average	ADJ
bracis-33554	264	22	reward	reward	NOUN
bracis-33554	264	23	,	,	PUNCT
bracis-33554	264	24	as	as	SCONJ
bracis-33554	264	25	demonstrated	demonstrate	VERB
bracis-33554	264	26	in	in	ADP
bracis-33554	264	27	the	the	DET
bracis-33554	264	28	numerical	numerical	ADJ
bracis-33554	264	29	examples	example	NOUN
bracis-33554	264	30	.	.	PUNCT
bracis-33554	265	1	as	as	ADV
bracis-33554	265	2	far	far	ADV
bracis-33554	265	3	as	as	SCONJ
bracis-33554	265	4	we	we	PRON
bracis-33554	265	5	know	know	VERB
bracis-33554	265	6	,	,	PUNCT
bracis-33554	265	7	there	there	PRON
bracis-33554	265	8	is	be	VERB
bracis-33554	265	9	no	no	DET
bracis-33554	265	10	work	work	NOUN
bracis-33554	265	11	in	in	ADP
bracis-33554	265	12	the	the	DET
bracis-33554	265	13	literature	literature	NOUN
bracis-33554	265	14	that	that	PRON
bracis-33554	265	15	characterizes	characterize	VERB
bracis-33554	265	16	cvar	cvar	NOUN
bracis-33554	265	17	for	for	ADP
bracis-33554	265	18	\(h=\infty	\(h=\infty	ADJ
bracis-33554	265	19	\	\	NOUN
bracis-33554	265	20	)	)	PUNCT
bracis-33554	265	21	.	.	PUNCT
bracis-33554	266	1	through	through	ADP
bracis-33554	266	2	numerical	numerical	ADJ
bracis-33554	266	3	experiments	experiment	NOUN
bracis-33554	266	4	,	,	PUNCT
bracis-33554	266	5	it	it	PRON
bracis-33554	266	6	was	be	AUX
bracis-33554	266	7	conjectured	conjecture	VERB
bracis-33554	266	8	that	that	SCONJ
bracis-33554	266	9	this	this	DET
bracis-33554	266	10	criterion	criterion	NOUN
bracis-33554	266	11	is	be	AUX
bracis-33554	266	12	equivalent	equivalent	ADJ
bracis-33554	266	13	to	to	ADP
bracis-33554	266	14	risk	risk	NOUN
bracis-33554	266	15	-	-	PUNCT
bracis-33554	266	16	neutral	neutral	ADJ
bracis-33554	266	17	,	,	PUNCT
bracis-33554	266	18	which	which	PRON
bracis-33554	266	19	needs	need	VERB
bracis-33554	266	20	to	to	PART
bracis-33554	266	21	be	be	AUX
bracis-33554	266	22	formally	formally	ADV
bracis-33554	266	23	demonstrated	demonstrate	VERB
bracis-33554	266	24	in	in	ADP
bracis-33554	266	25	future	future	ADJ
bracis-33554	266	26	work	work	NOUN
bracis-33554	266	27	.	.	PUNCT
bracis-33554	267	1	references	reference	NOUN
bracis-33554	267	2	ashok	ashok	NOUN
bracis-33554	267	3	,	,	PUNCT
bracis-33554	267	4	p.	p.	PROPN
bracis-33554	267	5	,	,	PUNCT
bracis-33554	267	6	chatterjee	chatterjee	PROPN
bracis-33554	267	7	,	,	PUNCT
bracis-33554	267	8	k.	k.	PROPN
bracis-33554	267	9	,	,	PUNCT
bracis-33554	267	10	daca	daca	PROPN
bracis-33554	267	11	,	,	PUNCT
bracis-33554	267	12	p.	p.	PROPN
bracis-33554	267	13	,	,	PUNCT
bracis-33554	267	14	křetínský	křetínský	PROPN
bracis-33554	267	15	,	,	PUNCT
bracis-33554	267	16	j.	j.	PROPN
bracis-33554	267	17	,	,	PUNCT
bracis-33554	267	18	meggendorfer	meggendorfer	VERB
bracis-33554	267	19	,	,	PUNCT
bracis-33554	267	20	t.	t.	NOUN
bracis-33554	267	21	:	:	PUNCT
bracis-33554	267	22	value	value	NOUN
bracis-33554	267	23	iteration	iteration	NOUN
bracis-33554	267	24	for	for	ADP
bracis-33554	267	25	long	long	ADV
bracis-33554	267	26	-	-	PUNCT
bracis-33554	267	27	run	run	VERB
bracis-33554	267	28	average	average	ADJ
bracis-33554	267	29	reward	reward	NOUN
bracis-33554	267	30	in	in	ADP
bracis-33554	267	31	markov	markov	NOUN
bracis-33554	267	32	decision	decision	NOUN
bracis-33554	267	33	processes	process	NOUN
bracis-33554	267	34	.	.	PUNCT
bracis-33554	268	1	in	in	ADP
bracis-33554	268	2	:	:	PUNCT
bracis-33554	268	3	majumdar	majumdar	PROPN
bracis-33554	268	4	,	,	PUNCT
bracis-33554	268	5	r.	r.	PROPN
bracis-33554	268	6	,	,	PUNCT
bracis-33554	268	7	kunčak	kunčak	NOUN
bracis-33554	268	8	,	,	PUNCT
bracis-33554	268	9	v.	v.	PROPN
bracis-33554	268	10	(	(	PUNCT
bracis-33554	268	11	eds	ed	NOUN
bracis-33554	268	12	.	.	PUNCT
bracis-33554	268	13	)	)	PUNCT
bracis-33554	268	14	computer	computer	NOUN
bracis-33554	268	15	aided	aid	VERB
bracis-33554	268	16	verification	verification	NOUN
bracis-33554	268	17	,	,	PUNCT
bracis-33554	268	18	pp	pp	ADJ
bracis-33554	268	19	.	.	PUNCT
bracis-33554	269	1	201–221	201–221	NUM
bracis-33554	269	2	.	.	PUNCT
bracis-33554	270	1	springer	springer	NOUN
bracis-33554	270	2	international	international	ADJ
bracis-33554	270	3	publishing	publishing	NOUN
bracis-33554	270	4	,	,	PUNCT
bracis-33554	270	5	cham	cham	PROPN
bracis-33554	270	6	(	(	PUNCT
bracis-33554	270	7	2017	2017	NUM
bracis-33554	270	8	)	)	PUNCT
bracis-33554	270	9	chapter	chapter	NOUN
bracis-33554	270	10	  	  	SPACE
bracis-33554	270	11	google	google	PROPN
bracis-33554	270	12	scholar	scholar	NOUN
bracis-33554	270	13	  	  	SPACE
bracis-33554	270	14	howard	howard	PROPN
bracis-33554	270	15	,	,	PUNCT
bracis-33554	270	16	r.a	r.a	PROPN
bracis-33554	270	17	.	.	PROPN
bracis-33554	270	18	,	,	PUNCT
bracis-33554	270	19	matheson	matheson	PROPN
bracis-33554	270	20	,	,	PUNCT
bracis-33554	270	21	j.e	j.e	PROPN
bracis-33554	270	22	.	.	PROPN
bracis-33554	270	23	:	:	PUNCT
bracis-33554	270	24	risk	risk	NOUN
bracis-33554	270	25	-	-	PUNCT
bracis-33554	270	26	sensitive	sensitive	ADJ
bracis-33554	270	27	markov	markov	NOUN
bracis-33554	270	28	decision	decision	NOUN
bracis-33554	270	29	processes	process	NOUN
bracis-33554	270	30	.	.	PUNCT
bracis-33554	271	1	manage	manage	VERB
bracis-33554	271	2	.	.	PUNCT
bracis-33554	272	1	sci	sci	PROPN
bracis-33554	272	2	.	.	PROPN
bracis-33554	272	3	18(7	18(7	NUM
bracis-33554	272	4	)	)	PUNCT
bracis-33554	272	5	,	,	PUNCT
bracis-33554	272	6	356–369	356–369	NUM
bracis-33554	272	7	(	(	PUNCT
bracis-33554	272	8	1972	1972	NUM
bracis-33554	272	9	)	)	PUNCT
bracis-33554	272	10	.	.	PUNCT
bracis-33554	273	1	http://www.jstor.org/stable/2629352	http://www.jstor.org/stable/2629352	PROPN
bracis-33554	273	2	perman	perman	PROPN
bracis-33554	273	3	,	,	PUNCT
bracis-33554	273	4	r.	r.	PROPN
bracis-33554	273	5	:	:	PUNCT
bracis-33554	273	6	natural	natural	ADJ
bracis-33554	273	7	resource	resource	NOUN
bracis-33554	273	8	and	and	CCONJ
bracis-33554	273	9	environmental	environmental	ADJ
bracis-33554	273	10	economics	economic	NOUN
bracis-33554	273	11	.	.	PUNCT
bracis-33554	274	1	pearson	pearson	PROPN
bracis-33554	274	2	education	education	PROPN
bracis-33554	274	3	(	(	PUNCT
bracis-33554	274	4	2003	2003	NUM
bracis-33554	274	5	)	)	PUNCT
bracis-33554	274	6	google	google	PROPN
bracis-33554	274	7	scholar	scholar	NOUN
bracis-33554	274	8	  	  	SPACE
bracis-33554	274	9	puterman	puterman	NOUN
bracis-33554	274	10	,	,	PUNCT
bracis-33554	274	11	m.l	m.l	PROPN
bracis-33554	274	12	.	.	PUNCT
bracis-33554	274	13	:	:	PUNCT
bracis-33554	274	14	markov	markov	NOUN
bracis-33554	274	15	decision	decision	NOUN
bracis-33554	274	16	processes	process	NOUN
bracis-33554	274	17	.	.	PUNCT
bracis-33554	275	1	wiley	wiley	PROPN
bracis-33554	275	2	series	series	PROPN
bracis-33554	275	3	in	in	ADP
bracis-33554	275	4	probability	probability	NOUN
bracis-33554	275	5	and	and	CCONJ
bracis-33554	275	6	mathematical	mathematical	ADJ
bracis-33554	275	7	statistics	statistic	NOUN
bracis-33554	275	8	,	,	PUNCT
bracis-33554	275	9	john	john	PROPN
bracis-33554	275	10	wiley	wiley	PROPN
bracis-33554	275	11	and	and	CCONJ
bracis-33554	275	12	sons	son	NOUN
bracis-33554	275	13	,	,	PUNCT
bracis-33554	275	14	new	new	PROPN
bracis-33554	275	15	york	york	PROPN
bracis-33554	275	16	(	(	PUNCT
bracis-33554	275	17	1994	1994	NUM
bracis-33554	275	18	)	)	PUNCT
bracis-33554	275	19	book	book	NOUN
bracis-33554	275	20	  	  	SPACE
bracis-33554	275	21	math	math	NOUN
bracis-33554	275	22	  	  	SPACE
bracis-33554	275	23	google	google	PROPN
bracis-33554	275	24	scholar	scholar	NOUN
bracis-33554	275	25	  	  	SPACE
bracis-33554	275	26	rockafellar	rockafellar	ADJ
bracis-33554	275	27	,	,	PUNCT
bracis-33554	275	28	r.t	r.t	PROPN
bracis-33554	275	29	.	.	PROPN
bracis-33554	275	30	,	,	PUNCT
bracis-33554	275	31	uryasev	uryasev	PROPN
bracis-33554	275	32	,	,	PUNCT
bracis-33554	275	33	s.	s.	PROPN
bracis-33554	275	34	,	,	PUNCT
bracis-33554	275	35	et	et	PROPN
bracis-33554	275	36	al	al	PROPN
bracis-33554	275	37	.	.	PUNCT
bracis-33554	275	38	:	:	PUNCT
bracis-33554	276	1	optimization	optimization	NOUN
bracis-33554	276	2	of	of	ADP
bracis-33554	276	3	conditional	conditional	ADJ
bracis-33554	276	4	value	value	NOUN
bracis-33554	276	5	-	-	PUNCT
bracis-33554	276	6	at	at	ADP
bracis-33554	276	7	-	-	PUNCT
bracis-33554	276	8	risk	risk	NOUN
bracis-33554	276	9	.	.	PUNCT
bracis-33554	277	1	j.	j.	PROPN
bracis-33554	277	2	risk	risk	PROPN
bracis-33554	277	3	2	2	NUM
bracis-33554	277	4	,	,	PUNCT
bracis-33554	277	5	21–42	21–42	NUM
bracis-33554	277	6	(	(	PUNCT
bracis-33554	277	7	2000	2000	NUM
bracis-33554	277	8	)	)	PUNCT
bracis-33554	277	9	article	article	NOUN
bracis-33554	277	10	  	  	SPACE
bracis-33554	277	11	math	math	NOUN
bracis-33554	277	12	  	  	SPACE
bracis-33554	277	13	google	google	PROPN
bracis-33554	277	14	scholar	scholar	NOUN
bracis-33554	277	15	  	  	SPACE
bracis-33554	277	16	rockafellar	rockafellar	ADJ
bracis-33554	277	17	,	,	PUNCT
bracis-33554	277	18	r.	r.	PROPN
bracis-33554	277	19	,	,	PUNCT
bracis-33554	277	20	uryasev	uryasev	PROPN
bracis-33554	277	21	,	,	PUNCT
bracis-33554	277	22	s.	s.	PROPN
bracis-33554	277	23	:	:	PUNCT
bracis-33554	277	24	conditional	conditional	ADJ
bracis-33554	277	25	value	value	NOUN
bracis-33554	277	26	-	-	PUNCT
bracis-33554	277	27	at	at	ADP
bracis-33554	277	28	-	-	PUNCT
bracis-33554	277	29	risk	risk	NOUN
bracis-33554	277	30	for	for	ADP
bracis-33554	277	31	general	general	ADJ
bracis-33554	277	32	loss	loss	NOUN
bracis-33554	277	33	distributions	distribution	NOUN
bracis-33554	277	34	.	.	PUNCT
bracis-33554	278	1	j.	j.	PROPN
bracis-33554	278	2	bank	bank	PROPN
bracis-33554	278	3	.	.	PUNCT
bracis-33554	279	1	fin	fin	NOUN
bracis-33554	279	2	.	.	PUNCT
bracis-33554	280	1	26(7	26(7	NUM
bracis-33554	280	2	)	)	PUNCT
bracis-33554	280	3	,	,	PUNCT
bracis-33554	280	4	1443–1471	1443–1471	NUM
bracis-33554	280	5	(	(	PUNCT
bracis-33554	280	6	2002	2002	NUM
bracis-33554	280	7	)	)	PUNCT
bracis-33554	280	8	article	article	NOUN
bracis-33554	280	9	  	  	SPACE
bracis-33554	280	10	math	math	NOUN
bracis-33554	280	11	  	  	SPACE
bracis-33554	280	12	google	google	PROPN
bracis-33554	280	13	scholar	scholar	NOUN
bracis-33554	280	14	  	  	SPACE
bracis-33554	280	15	xia	xia	PROPN
bracis-33554	280	16	,	,	PUNCT
bracis-33554	280	17	l.	l.	PROPN
bracis-33554	280	18	,	,	PUNCT
bracis-33554	280	19	zhang	zhang	PROPN
bracis-33554	280	20	,	,	PUNCT
bracis-33554	280	21	l.	l.	PROPN
bracis-33554	280	22	,	,	PUNCT
bracis-33554	280	23	glynn	glynn	PROPN
bracis-33554	280	24	,	,	PUNCT
bracis-33554	280	25	p.w	p.w	PROPN
bracis-33554	280	26	.	.	PROPN
bracis-33554	280	27	:	:	PUNCT
bracis-33554	280	28	risk	risk	NOUN
bracis-33554	280	29	-	-	PUNCT
bracis-33554	280	30	sensitive	sensitive	ADJ
bracis-33554	280	31	markov	markov	NOUN
bracis-33554	280	32	decision	decision	NOUN
bracis-33554	280	33	processes	process	NOUN
bracis-33554	280	34	with	with	ADP
bracis-33554	280	35	long	long	ADV
bracis-33554	280	36	-	-	PUNCT
bracis-33554	280	37	run	run	VERB
bracis-33554	280	38	cvar	cvar	NOUN
bracis-33554	280	39	criterion	criterion	NOUN
bracis-33554	280	40	.	.	PUNCT
bracis-33554	281	1	prod	prod	NOUN
bracis-33554	281	2	.	.	PUNCT
bracis-33554	282	1	oper	oper	PROPN
bracis-33554	282	2	.	.	PROPN
bracis-33554	282	3	manag	manag	PROPN
bracis-33554	282	4	.	.	PUNCT
bracis-33554	283	1	32(12	32(12	NUM
bracis-33554	283	2	)	)	PUNCT
bracis-33554	284	1	,	,	PUNCT
bracis-33554	284	2	4049–4067	4049–4067	NUM
bracis-33554	284	3	(	(	PUNCT
bracis-33554	284	4	2023	2023	NUM
bracis-33554	284	5	)	)	PUNCT
bracis-33554	284	6	article	article	NOUN
bracis-33554	284	7	  	  	SPACE
bracis-33554	284	8	math	math	NOUN
bracis-33554	284	9	  	  	SPACE
bracis-33554	284	10	google	google	PROPN
bracis-33554	284	11	scholar	scholar	NOUN
bracis-33554	284	12	  	  	SPACE
bracis-33554	284	13	download	download	NOUN
bracis-33554	284	14	references	reference	NOUN
bracis-33554	284	15	acknowledgments	acknowledgment	NOUN
bracis-33554	284	16	this	this	DET
bracis-33554	284	17	study	study	NOUN
bracis-33554	284	18	was	be	AUX
bracis-33554	284	19	supported	support	VERB
bracis-33554	284	20	in	in	ADP
bracis-33554	284	21	part	part	NOUN
bracis-33554	284	22	by	by	ADP
bracis-33554	284	23	the	the	DET
bracis-33554	284	24	coordenação	coordenação	PROPN
bracis-33554	284	25	de	de	PROPN
bracis-33554	284	26	aperfeiçoamento	aperfeiçoamento	PROPN
bracis-33554	284	27	de	de	X
bracis-33554	284	28	pessoal	pessoal	PROPN
bracis-33554	284	29	de	de	PROPN
bracis-33554	284	30	nível	nível	PROPN
bracis-33554	284	31	superior	superior	ADJ
bracis-33554	284	32	(	(	PUNCT
bracis-33554	284	33	capes	cape	NOUN
bracis-33554	284	34	)	)	PUNCT
bracis-33554	284	35	–	–	PUNCT
bracis-33554	284	36	finance	finance	NOUN
bracis-33554	284	37	code	code	NOUN
bracis-33554	284	38	001	001	NOUN
bracis-33554	284	39	,	,	PUNCT
bracis-33554	284	40	by	by	ADP
bracis-33554	284	41	the	the	DET
bracis-33554	284	42	são	são	PROPN
bracis-33554	284	43	paulo	paulo	PROPN
bracis-33554	284	44	research	research	PROPN
bracis-33554	284	45	foundation	foundation	PROPN
bracis-33554	284	46	(	(	PUNCT
bracis-33554	284	47	fapesp	fapesp	NOUN
bracis-33554	284	48	)	)	PUNCT
bracis-33554	284	49	grant	grant	NOUN
bracis-33554	284	50	\(\#\)2018/11236	\(\#\)2018/11236	NOUN
bracis-33554	284	51	-	-	SYM
bracis-33554	284	52	9	9	NUM
bracis-33554	284	53	and	and	CCONJ
bracis-33554	284	54	the	the	DET
bracis-33554	284	55	center	center	NOUN
bracis-33554	284	56	for	for	ADP
bracis-33554	284	57	artificial	artificial	ADJ
bracis-33554	284	58	intelligence	intelligence	NOUN
bracis-33554	284	59	(	(	PUNCT
bracis-33554	284	60	c4ai	c4ai	NOUN
bracis-33554	284	61	-	-	PUNCT
bracis-33554	284	62	usp	usp	NOUN
bracis-33554	284	63	)	)	PUNCT
bracis-33554	284	64	,	,	PUNCT
bracis-33554	284	65	with	with	ADP
bracis-33554	284	66	support	support	NOUN
bracis-33554	284	67	by	by	ADP
bracis-33554	284	68	fapesp	fapesp	NOUN
bracis-33554	284	69	(	(	PUNCT
bracis-33554	284	70	grant	grant	VERB
bracis-33554	284	71	#	#	SYM
bracis-33554	284	72	2019/07665	2019/07665	NUM
bracis-33554	284	73	-	-	SYM
bracis-33554	284	74	4	4	NUM
bracis-33554	284	75	)	)	PUNCT
bracis-33554	284	76	and	and	CCONJ
bracis-33554	284	77	by	by	ADP
bracis-33554	284	78	the	the	DET
bracis-33554	284	79	ibm	ibm	PROPN
bracis-33554	284	80	corporation	corporation	NOUN
bracis-33554	284	81	.	.	PUNCT
bracis-33554	285	1	author	author	NOUN
bracis-33554	285	2	information	information	NOUN
bracis-33554	285	3	authors	author	NOUN
bracis-33554	285	4	and	and	CCONJ
bracis-33554	285	5	affiliations	affiliation	NOUN
bracis-33554	285	6	university	university	PROPN
bracis-33554	285	7	of	of	ADP
bracis-33554	285	8	são	são	PROPN
bracis-33554	285	9	paulo	paulo	PROPN
bracis-33554	285	10	,	,	PUNCT
bracis-33554	285	11	cidade	cidade	NOUN
bracis-33554	285	12	universitária	universitária	PROPN
bracis-33554	285	13	,	,	PUNCT
bracis-33554	285	14	butantã	butantã	ADV
bracis-33554	285	15	,	,	PUNCT
bracis-33554	285	16	são	são	PROPN
bracis-33554	285	17	paulo	paulo	PROPN
bracis-33554	285	18	,	,	PUNCT
bracis-33554	285	19	sp	sp	NOUN
bracis-33554	285	20	,	,	PUNCT
bracis-33554	285	21	05508	05508	NUM
bracis-33554	285	22	-	-	SYM
bracis-33554	285	23	220	220	NUM
bracis-33554	285	24	,	,	PUNCT
bracis-33554	285	25	brazil	brazil	PROPN
bracis-33554	285	26	willy	willy	PROPN
bracis-33554	285	27	arthur	arthur	PROPN
bracis-33554	285	28	silva	silva	PROPN
bracis-33554	285	29	reis	reis	PROPN
bracis-33554	285	30	,	,	PUNCT
bracis-33554	285	31	 	 	SPACE
bracis-33554	285	32	karina	karina	PROPN
bracis-33554	285	33	valdivia	valdivia	PROPN
bracis-33554	285	34	delgado	delgado	PROPN
bracis-33554	285	35	 	 	SPACE
bracis-33554	285	36	&	&	CCONJ
bracis-33554	285	37	 	 	SPACE
bracis-33554	285	38	valdinei	valdinei	PROPN
bracis-33554	285	39	freire	freire	PROPN
bracis-33554	285	40	authors	author	NOUN
bracis-33554	285	41	willy	willy	PROPN
bracis-33554	285	42	arthur	arthur	PROPN
bracis-33554	285	43	silva	silva	PROPN
bracis-33554	285	44	reisview	reisview	PROPN
bracis-33554	285	45	author	author	NOUN
bracis-33554	285	46	publications	publication	NOUN
bracis-33554	285	47	search	search	NOUN
bracis-33554	285	48	author	author	NOUN
bracis-33554	285	49	on	on	ADP
bracis-33554	285	50	:	:	PUNCT
bracis-33554	285	51	pubmed	pubmed	PROPN
bracis-33554	285	52	 	 	SPACE
bracis-33554	285	53	google	google	PROPN
bracis-33554	285	54	scholar	scholar	PROPN
bracis-33554	285	55	karina	karina	PROPN
bracis-33554	285	56	valdivia	valdivia	PROPN
bracis-33554	285	57	delgadoview	delgadoview	PROPN
bracis-33554	285	58	author	author	NOUN
bracis-33554	285	59	publications	publication	NOUN
bracis-33554	285	60	search	search	NOUN
bracis-33554	285	61	author	author	NOUN
bracis-33554	285	62	on	on	ADP
bracis-33554	285	63	:	:	PUNCT
bracis-33554	285	64	pubmed	pubmed	PROPN
bracis-33554	285	65	 	 	SPACE
bracis-33554	285	66	google	google	PROPN
bracis-33554	285	67	scholar	scholar	NOUN
bracis-33554	285	68	valdinei	valdinei	NOUN
bracis-33554	285	69	freireview	freireview	NOUN
bracis-33554	285	70	author	author	NOUN
bracis-33554	285	71	publications	publication	NOUN
bracis-33554	285	72	search	search	NOUN
bracis-33554	285	73	author	author	NOUN
bracis-33554	285	74	on	on	ADP
bracis-33554	285	75	:	:	PUNCT
bracis-33554	285	76	pubmed	pubmed	PROPN
bracis-33554	285	77	 	 	SPACE
bracis-33554	285	78	google	google	PROPN
bracis-33554	285	79	scholar	scholar	NOUN
bracis-33554	285	80	corresponding	correspond	VERB
bracis-33554	285	81	author	author	NOUN
bracis-33554	285	82	correspondence	correspondence	NOUN
bracis-33554	285	83	to	to	ADP
bracis-33554	285	84	willy	willy	PROPN
bracis-33554	285	85	arthur	arthur	PROPN
bracis-33554	285	86	silva	silva	PROPN
bracis-33554	285	87	reis	reis	PROPN
bracis-33554	285	88	.	.	PUNCT
bracis-33554	286	1	editor	editor	NOUN
bracis-33554	286	2	information	information	NOUN
bracis-33554	286	3	editors	editor	NOUN
bracis-33554	286	4	and	and	CCONJ
bracis-33554	286	5	affiliations	affiliation	NOUN
bracis-33554	286	6	universidade	universidade	VERB
bracis-33554	286	7	federal	federal	PROPN
bracis-33554	286	8	fluminense	fluminense	PROPN
bracis-33554	286	9	,	,	PUNCT
bracis-33554	286	10	niterói	niterói	PROPN
bracis-33554	286	11	,	,	PUNCT
bracis-33554	286	12	brazil	brazil	PROPN
bracis-33554	286	13	aline	aline	PROPN
bracis-33554	286	14	paes	paes	PROPN
bracis-33554	286	15	instituto	instituto	PROPN
bracis-33554	286	16	tecnológico	tecnológico	PROPN
bracis-33554	286	17	de	de	PROPN
bracis-33554	286	18	aeronáutica	aeronáutica	PROPN
bracis-33554	286	19	,	,	PUNCT
bracis-33554	286	20	são	são	PROPN
bracis-33554	286	21	josé	josé	PROPN
bracis-33554	286	22	dos	dos	PROPN
bracis-33554	286	23	campos	campos	PROPN
bracis-33554	286	24	,	,	PUNCT
bracis-33554	286	25	brazil	brazil	PROPN
bracis-33554	286	26	filipe	filipe	PROPN
bracis-33554	286	27	a.	a.	PROPN
bracis-33554	286	28	n.	n.	PROPN
bracis-33554	286	29	verri	verri	PROPN
bracis-33554	286	30	rights	right	NOUN
bracis-33554	286	31	and	and	CCONJ
bracis-33554	286	32	permissions	permission	NOUN
bracis-33554	286	33	reprints	reprint	NOUN
bracis-33554	286	34	and	and	CCONJ
bracis-33554	286	35	permissions	permission	VERB
bracis-33554	286	36	copyright	copyright	NOUN
bracis-33554	286	37	information	information	NOUN
bracis-33554	286	38	©	©	ADP
bracis-33554	286	39	2025	2025	NUM
bracis-33554	286	40	the	the	DET
bracis-33554	286	41	author(s	author(s	NOUN
bracis-33554	286	42	)	)	PUNCT
bracis-33554	286	43	,	,	PUNCT
bracis-33554	286	44	under	under	ADP
bracis-33554	286	45	exclusive	exclusive	ADJ
bracis-33554	286	46	license	license	NOUN
bracis-33554	286	47	to	to	ADP
bracis-33554	286	48	springer	springer	NOUN
bracis-33554	286	49	nature	nature	PROPN
bracis-33554	286	50	switzerland	switzerland	PROPN
bracis-33554	286	51	ag	ag	PROPN
bracis-33554	286	52	about	about	ADP
bracis-33554	286	53	this	this	DET
bracis-33554	286	54	paper	paper	NOUN
bracis-33554	286	55	cite	cite	VERB
bracis-33554	286	56	this	this	DET
bracis-33554	286	57	paper	paper	NOUN
bracis-33554	286	58	reis	reis	NOUN
bracis-33554	286	59	,	,	PUNCT
bracis-33554	286	60	w.a.s	w.a.s	PROPN
bracis-33554	286	61	.	.	PROPN
bracis-33554	286	62	,	,	PUNCT
bracis-33554	286	63	delgado	delgado	PROPN
bracis-33554	286	64	,	,	PUNCT
bracis-33554	286	65	k.v	k.v	PROPN
bracis-33554	286	66	.	.	PROPN
bracis-33554	286	67	,	,	PUNCT
bracis-33554	286	68	freire	freire	PROPN
bracis-33554	286	69	,	,	PUNCT
bracis-33554	286	70	v.	v.	PROPN
bracis-33554	286	71	(	(	PUNCT
bracis-33554	286	72	2025	2025	NUM
bracis-33554	286	73	)	)	PUNCT
bracis-33554	286	74	.	.	PUNCT
bracis-33554	287	1	a	a	DET
bracis-33554	287	2	unified	unify	VERB
bracis-33554	287	3	framework	framework	NOUN
bracis-33554	287	4	for	for	ADP
bracis-33554	287	5	average	average	ADJ
bracis-33554	287	6	reward	reward	NOUN
bracis-33554	287	7	criterion	criterion	NOUN
bracis-33554	287	8	and	and	CCONJ
bracis-33554	287	9	risk	risk	NOUN
bracis-33554	287	10	.	.	PUNCT
bracis-33554	288	1	in	in	ADP
bracis-33554	288	2	:	:	PUNCT
bracis-33554	288	3	paes	paes	PROPN
bracis-33554	288	4	,	,	PUNCT
bracis-33554	288	5	a.	a.	PROPN
bracis-33554	288	6	,	,	PUNCT
bracis-33554	288	7	verri	verri	NOUN
bracis-33554	288	8	,	,	PUNCT
bracis-33554	288	9	f.a.n	f.a.n	ADJ
bracis-33554	288	10	.	.	PUNCT
bracis-33554	288	11	(	(	PUNCT
bracis-33554	288	12	eds	ed	NOUN
bracis-33554	288	13	)	)	PUNCT
bracis-33554	288	14	intelligent	intelligent	ADJ
bracis-33554	288	15	systems	system	NOUN
bracis-33554	288	16	.	.	PUNCT
bracis-33554	288	17	bracis	bracis	PROPN
bracis-33554	288	18	2024	2024	NUM
bracis-33554	288	19	.	.	PUNCT
bracis-33554	289	1	lecture	lecture	NOUN
bracis-33554	289	2	notes	note	NOUN
bracis-33554	289	3	in	in	ADP
bracis-33554	289	4	computer	computer	NOUN
bracis-33554	289	5	science	science	NOUN
bracis-33554	289	6	(	(	PUNCT
bracis-33554	289	7	)	)	PUNCT
bracis-33554	289	8	,	,	PUNCT
bracis-33554	289	9	vol	vol	NOUN
bracis-33554	289	10	15412	15412	NUM
bracis-33554	289	11	.	.	PUNCT
bracis-33554	290	1	springer	springer	NOUN
bracis-33554	290	2	,	,	PUNCT
bracis-33554	290	3	cham	cham	PROPN
bracis-33554	290	4	.	.	PUNCT
bracis-33554	291	1	https://doi.org/10.1007/978-3-031-79029-4_7	https://doi.org/10.1007/978-3-031-79029-4_7	PUNCT
bracis-33554	292	1	download	download	NOUN
bracis-33554	292	2	citation	citation	NOUN
bracis-33554	292	3	.ris	.ris	PUNCT
bracis-33554	292	4	.enw	.enw	PROPN
bracis-33554	293	1	.bib	.bib	PUNCT
bracis-33554	293	2	doi	doi	PROPN
bracis-33554	293	3	:	:	PUNCT
bracis-33554	293	4	https://doi.org/10.1007/978-3-031-79029-4_7	https://doi.org/10.1007/978-3-031-79029-4_7	X
bracis-33554	293	5	published	publish	VERB
bracis-33554	293	6	:	:	PUNCT
bracis-33554	293	7	30	30	NUM
bracis-33554	293	8	january	january	PROPN
bracis-33554	293	9	2025	2025	NUM
bracis-33554	293	10	publisher	publisher	NOUN
bracis-33554	293	11	name	name	NOUN
bracis-33554	293	12	:	:	PUNCT
bracis-33554	293	13	springer	springer	NOUN
bracis-33554	293	14	,	,	PUNCT
bracis-33554	293	15	cham	cham	PROPN
bracis-33554	293	16	print	print	PROPN
bracis-33554	293	17	isbn	isbn	PROPN
bracis-33554	293	18	:	:	PUNCT
bracis-33554	293	19	978	978	NUM
bracis-33554	293	20	-	-	SYM
bracis-33554	293	21	3	3	NUM
bracis-33554	293	22	-	-	PUNCT
bracis-33554	293	23	031	031	NUM
bracis-33554	293	24	-	-	PUNCT
bracis-33554	293	25	79028	79028	NUM
bracis-33554	293	26	-	-	SYM
bracis-33554	293	27	7	7	NUM
bracis-33554	293	28	online	online	ADJ
bracis-33554	293	29	isbn	isbn	NOUN
bracis-33554	293	30	:	:	PUNCT
bracis-33554	293	31	978	978	NUM
bracis-33554	293	32	-	-	SYM
bracis-33554	293	33	3	3	NUM
bracis-33554	293	34	-	-	PUNCT
bracis-33554	293	35	031	031	NUM
bracis-33554	293	36	-	-	PUNCT
bracis-33554	293	37	79029	79029	NUM
bracis-33554	293	38	-	-	SYM
bracis-33554	293	39	4	4	NUM
bracis-33554	293	40	ebook	ebook	NOUN
bracis-33554	293	41	packages	package	NOUN
bracis-33554	293	42	:	:	PUNCT
bracis-33554	293	43	computer	computer	NOUN
bracis-33554	293	44	sciencecomputer	sciencecomputer	NOUN
bracis-33554	293	45	science	science	NOUN
bracis-33554	293	46	(	(	PUNCT
bracis-33554	293	47	r0	r0	NOUN
bracis-33554	293	48	)	)	PUNCT
bracis-33554	293	49	share	share	VERB
bracis-33554	293	50	this	this	DET
bracis-33554	293	51	paper	paper	NOUN
bracis-33554	293	52	anyone	anyone	PRON
bracis-33554	293	53	you	you	PRON
bracis-33554	293	54	share	share	VERB
bracis-33554	293	55	the	the	DET
bracis-33554	293	56	following	follow	VERB
bracis-33554	293	57	link	link	NOUN
bracis-33554	293	58	with	with	ADP
bracis-33554	293	59	will	will	AUX
bracis-33554	293	60	be	be	AUX
bracis-33554	293	61	able	able	ADJ
bracis-33554	293	62	to	to	PART
bracis-33554	293	63	read	read	VERB
bracis-33554	293	64	this	this	DET
bracis-33554	293	65	content	content	NOUN
bracis-33554	293	66	:	:	PUNCT
bracis-33554	293	67	get	get	VERB
bracis-33554	293	68	shareable	shareable	ADJ
bracis-33554	293	69	linksorry	linksorry	NOUN
bracis-33554	293	70	,	,	PUNCT
bracis-33554	293	71	a	a	DET
bracis-33554	293	72	shareable	shareable	ADJ
bracis-33554	293	73	link	link	NOUN
bracis-33554	293	74	is	be	AUX
bracis-33554	293	75	not	not	PART
bracis-33554	293	76	currently	currently	ADV
bracis-33554	293	77	available	available	ADJ
bracis-33554	293	78	for	for	ADP
bracis-33554	293	79	this	this	DET
bracis-33554	293	80	article	article	NOUN
bracis-33554	293	81	.	.	PUNCT
bracis-33554	294	1	copy	copy	VERB
bracis-33554	294	2	shareable	shareable	ADJ
bracis-33554	294	3	link	link	NOUN
bracis-33554	294	4	to	to	PART
bracis-33554	294	5	clipboard	clipboard	NOUN
bracis-33554	294	6	provided	provide	VERB
bracis-33554	294	7	by	by	ADP
bracis-33554	294	8	the	the	DET
bracis-33554	294	9	springer	springer	NOUN
bracis-33554	294	10	nature	nature	PROPN
bracis-33554	294	11	sharedit	sharedit	PROPN
bracis-33554	294	12	content	content	NOUN
bracis-33554	294	13	-	-	PUNCT
bracis-33554	294	14	sharing	share	VERB
bracis-33554	294	15	initiative	initiative	NOUN
bracis-33554	294	16	keywords	keyword	NOUN
bracis-33554	294	17	markov	markov	NOUN
bracis-33554	294	18	decision	decision	NOUN
bracis-33554	294	19	process	process	NOUN
bracis-33554	294	20	average	average	ADJ
bracis-33554	294	21	reward	reward	NOUN
bracis-33554	294	22	risk	risk	NOUN
bracis-33554	294	23	-	-	PUNCT
bracis-33554	294	24	sensitive	sensitive	ADJ
bracis-33554	294	25	publish	publish	NOUN
bracis-33554	294	26	with	with	ADP
bracis-33554	294	27	us	us	PROPN
bracis-33554	294	28	policies	policy	NOUN
bracis-33554	294	29	and	and	CCONJ
bracis-33554	294	30	ethics	ethic	NOUN
bracis-33554	294	31	search	search	NOUN
bracis-33554	294	32	search	search	NOUN
bracis-33554	294	33	by	by	ADP
bracis-33554	294	34	keyword	keyword	NOUN
bracis-33554	294	35	or	or	CCONJ
bracis-33554	294	36	author	author	NOUN
bracis-33554	294	37	search	search	NOUN
bracis-33554	294	38	navigation	navigation	NOUN
bracis-33554	294	39	find	find	VERB
bracis-33554	294	40	a	a	DET
bracis-33554	294	41	journal	journal	NOUN
bracis-33554	294	42	publish	publish	VERB
bracis-33554	294	43	with	with	ADP
bracis-33554	294	44	us	we	PRON
bracis-33554	294	45	track	track	VERB
bracis-33554	294	46	your	your	PRON
bracis-33554	294	47	research	research	NOUN
bracis-33554	294	48	discover	discover	VERB
bracis-33554	294	49	content	content	NOUN
bracis-33554	294	50	journals	journal	NOUN
bracis-33554	294	51	a	a	DET
bracis-33554	294	52	-	-	PUNCT
bracis-33554	294	53	z	z	NOUN
bracis-33554	294	54	books	book	NOUN
bracis-33554	294	55	a	a	DET
bracis-33554	294	56	-	-	PUNCT
bracis-33554	294	57	z	z	NOUN
bracis-33554	294	58	publish	publish	NOUN
bracis-33554	294	59	with	with	ADP
bracis-33554	294	60	us	us	PROPN
bracis-33554	294	61	journal	journal	PROPN
bracis-33554	294	62	finder	finder	PROPN
bracis-33554	294	63	publish	publish	VERB
bracis-33554	294	64	your	your	PRON
bracis-33554	294	65	research	research	NOUN
bracis-33554	294	66	language	language	NOUN
bracis-33554	294	67	editing	edit	VERB
bracis-33554	294	68	open	open	ADJ
bracis-33554	294	69	access	access	NOUN
bracis-33554	294	70	publishing	publishing	NOUN
bracis-33554	294	71	products	product	NOUN
bracis-33554	294	72	and	and	CCONJ
bracis-33554	294	73	services	service	NOUN
bracis-33554	294	74	our	our	PRON
bracis-33554	294	75	products	product	NOUN
bracis-33554	294	76	librarians	librarian	VERB
bracis-33554	294	77	societies	society	NOUN
bracis-33554	294	78	partners	partner	NOUN
bracis-33554	294	79	and	and	CCONJ
bracis-33554	294	80	advertisers	advertiser	NOUN
bracis-33554	294	81	our	our	PRON
bracis-33554	294	82	brands	brand	NOUN
bracis-33554	294	83	springer	springer	NOUN
bracis-33554	294	84	nature	nature	PROPN
bracis-33554	294	85	portfolio	portfolio	PROPN
bracis-33554	294	86	bmc	bmc	PROPN
bracis-33554	294	87	palgrave	palgrave	PROPN
bracis-33554	294	88	macmillan	macmillan	PROPN
bracis-33554	294	89	apress	apress	PROPN
bracis-33554	294	90	discover	discover	VERB
bracis-33554	294	91	your	your	PRON
bracis-33554	294	92	privacy	privacy	NOUN
bracis-33554	294	93	choices	choice	NOUN
bracis-33554	294	94	/	/	SYM
bracis-33554	294	95	manage	manage	NOUN
bracis-33554	294	96	cookies	cookie	NOUN
bracis-33554	294	97	your	your	PRON
bracis-33554	294	98	us	us	PROPN
bracis-33554	295	1	state	state	NOUN
bracis-33554	295	2	privacy	privacy	NOUN
bracis-33554	295	3	rights	right	NOUN
bracis-33554	295	4	accessibility	accessibility	NOUN
bracis-33554	295	5	statement	statement	NOUN
bracis-33554	295	6	terms	term	NOUN
bracis-33554	295	7	and	and	CCONJ
bracis-33554	295	8	conditions	condition	NOUN
bracis-33554	295	9	privacy	privacy	NOUN
bracis-33554	295	10	policy	policy	NOUN
bracis-33554	295	11	help	help	NOUN
bracis-33554	295	12	and	and	CCONJ
bracis-33554	295	13	support	support	VERB
bracis-33554	295	14	legal	legal	ADJ
bracis-33554	295	15	notice	notice	NOUN
bracis-33554	295	16	cancel	cancel	VERB
bracis-33554	295	17	contracts	contract	NOUN
bracis-33554	295	18	here	here	ADV
bracis-33554	295	19	129.74.145.123	129.74.145.123	NUM
bracis-33554	295	20	hesburgh	hesburgh	PROPN
bracis-33554	295	21	library	library	PROPN
bracis-33554	295	22	er	er	INTJ
bracis-33554	295	23	unit	unit	NOUN
bracis-33554	295	24	(	(	PUNCT
bracis-33554	295	25	3005732405	3005732405	NUM
bracis-33554	295	26	)	)	PUNCT
bracis-33554	295	27	northeast	northeast	ADJ
bracis-33554	295	28	research	research	NOUN
bracis-33554	295	29	libraries	library	NOUN
bracis-33554	295	30	(	(	PUNCT
bracis-33554	295	31	nerl	nerl	PROPN
bracis-33554	295	32	)	)	PUNCT
bracis-33554	295	33	(	(	PUNCT
bracis-33554	295	34	8200828607	8200828607	NUM
bracis-33554	295	35	)	)	PUNCT
bracis-33554	295	36	nerl	nerl	VERB
bracis-33554	295	37	ta	ta	X
bracis-33554	295	38	account	account	NOUN
bracis-33554	295	39	(	(	PUNCT
bracis-33554	295	40	3006206169	3006206169	NUM
bracis-33554	295	41	)	)	PUNCT
bracis-33554	295	42	university	university	NOUN
bracis-33554	295	43	of	of	ADP
bracis-33554	295	44	notre	notre	PROPN
bracis-33554	295	45	dame	dame	PROPN
bracis-33554	295	46	hesburgh	hesburgh	PROPN
bracis-33554	295	47	library	library	NOUN
bracis-33554	295	48	(	(	PUNCT
bracis-33554	295	49	3000184373	3000184373	NUM
bracis-33554	295	50	)	)	PUNCT
bracis-33554	296	1	©	©	ADP
bracis-33554	296	2	2025	2025	NUM
bracis-33554	296	3	springer	springer	NOUN
bracis-33554	296	4	nature	nature	NOUN