{"id":"https://openalex.org/W4390827214","doi":"https://doi.org/10.1137/23m1572398","title":"Extreme Occupation Measures in Markov Decision Processes with an Absorbing State","display_name":"Extreme Occupation Measures in Markov Decision Processes with an Absorbing State","publication_year":2024,"publication_date":"2024-01-12","ids":{"openalex":"https://openalex.org/W4390827214","doi":"https://doi.org/10.1137/23m1572398"},"language":"en","primary_location":{"id":"doi:10.1137/23m1572398","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1572398","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://pure-oai.bham.ac.uk/ws/files/220423268/PiunovskiyA2024Extreme.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054092600","display_name":"Alexey Piunovskiy","orcid":"https://orcid.org/0000-0002-9683-4856"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alexey Piunovskiy","raw_affiliation_strings":["Corresponding author. Department of Mathematical Sciences, University of Liverpool, L69 7ZL Liverpool, UK"],"affiliations":[{"raw_affiliation_string":"Corresponding author. Department of Mathematical Sciences, University of Liverpool, L69 7ZL Liverpool, UK","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036373241","display_name":"Yi Zhang","orcid":"https://orcid.org/0000-0002-3200-6306"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yi Zhang","raw_affiliation_strings":["School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK","institution_ids":["https://openalex.org/I79619799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054092600"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9458,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.89511834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"62","issue":"1","first_page":"65","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11195","display_name":"Simulation Techniques and Applications","score":0.9664999842643738,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8327526450157166},{"id":"https://openalex.org/keywords/polish-space","display_name":"Polish space","score":0.6286365389823914},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.6136038303375244},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.6000356674194336},{"id":"https://openalex.org/keywords/borel-measure","display_name":"Borel measure","score":0.5809262990951538},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5435608625411987},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5331090688705444},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5189887881278992},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4996337890625},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.47925782203674316},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4759249985218048},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.46414509415626526},{"id":"https://openalex.org/keywords/extreme-point","display_name":"Extreme point","score":0.45098456740379333},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.44707316160202026},{"id":"https://openalex.org/keywords/markov-kernel","display_name":"Markov kernel","score":0.4194856286048889},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3632446825504303},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3383313715457916},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.2925013601779938},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24599823355674744},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.22369423508644104},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1456676721572876},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.13022345304489136},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11373576521873474},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10126852989196777},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08217215538024902}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8327526450157166},{"id":"https://openalex.org/C31316033","wikidata":"https://www.wikidata.org/wiki/Q1207972","display_name":"Polish space","level":3,"score":0.6286365389823914},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.6136038303375244},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.6000356674194336},{"id":"https://openalex.org/C166758865","wikidata":"https://www.wikidata.org/wiki/Q892585","display_name":"Borel measure","level":3,"score":0.5809262990951538},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5435608625411987},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5331090688705444},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5189887881278992},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4996337890625},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.47925782203674316},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4759249985218048},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.46414509415626526},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.45098456740379333},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.44707316160202026},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.4194856286048889},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3632446825504303},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3383313715457916},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.2925013601779938},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24599823355674744},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.22369423508644104},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1456676721572876},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.13022345304489136},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11373576521873474},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10126852989196777},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08217215538024902},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/23m1572398","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1572398","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/05ae9ccd-7986-42d0-83eb-71f2fbb91586","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/05ae9ccd-7986-42d0-83eb-71f2fbb91586","pdf_url":"https://pure-oai.bham.ac.uk/ws/files/220423268/PiunovskiyA2024Extreme.pdf","source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Piunovskiy , A & Zhang , Y 2024 , ' Extreme occupation measures in Markov decision processes with an absorbing state ' , SIAM Journal on Control and Optimization , vol. 62 , no. 1 , pp. 65-90 . https://doi.org/10.1137/23M1572398","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/05ae9ccd-7986-42d0-83eb-71f2fbb91586","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/05ae9ccd-7986-42d0-83eb-71f2fbb91586","pdf_url":"https://pure-oai.bham.ac.uk/ws/files/220423268/PiunovskiyA2024Extreme.pdf","source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Piunovskiy , A & Zhang , Y 2024 , ' Extreme occupation measures in Markov decision processes with an absorbing state ' , SIAM Journal on Control and Optimization , vol. 62 , no. 1 , pp. 65-90 . https://doi.org/10.1137/23M1572398","raw_type":"article"},"sustainable_development_goals":[{"score":0.8100000023841858,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G329129971","display_name":null,"funder_award_id":"EP/T018216/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390827214.pdf","grobid_xml":"https://content.openalex.org/works/W4390827214.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W118602349","https://openalex.org/W323116121","https://openalex.org/W1200801359","https://openalex.org/W1518072521","https://openalex.org/W1518931405","https://openalex.org/W1524028581","https://openalex.org/W1973918939","https://openalex.org/W1991591460","https://openalex.org/W1991625634","https://openalex.org/W2004640191","https://openalex.org/W2010654234","https://openalex.org/W2013479759","https://openalex.org/W2028198084","https://openalex.org/W2030565368","https://openalex.org/W2030974365","https://openalex.org/W2033830101","https://openalex.org/W2049032169","https://openalex.org/W2056512386","https://openalex.org/W2058577181","https://openalex.org/W2070935253","https://openalex.org/W2123649906","https://openalex.org/W2139261921","https://openalex.org/W2264543683","https://openalex.org/W2278927785","https://openalex.org/W2323793148","https://openalex.org/W2335062971","https://openalex.org/W2339816922","https://openalex.org/W2924486842","https://openalex.org/W2963622571","https://openalex.org/W2964207797","https://openalex.org/W2978834951","https://openalex.org/W2999555829","https://openalex.org/W3140571750","https://openalex.org/W4200635901","https://openalex.org/W4210545817","https://openalex.org/W4229597915","https://openalex.org/W4255925811","https://openalex.org/W4385336893"],"related_works":["https://openalex.org/W2143225908","https://openalex.org/W2339308614","https://openalex.org/W1590726137","https://openalex.org/W2075985877","https://openalex.org/W2007418879","https://openalex.org/W2894014085","https://openalex.org/W1975855422","https://openalex.org/W1980961056","https://openalex.org/W1963872190","https://openalex.org/W2393061156"],"abstract_inverted_index":{"In":[0],"this":[1,78,120],"paper,":[2],"we":[3,62,80],"consider":[4,35,81],"a":[5,11,29,73,82,126],"Markov":[6],"decision":[7],"process":[8],"(MDP)":[9],"with":[10,85],"Borel":[12,30],"state":[13,26],"space":[14,32,37],"X":[15,44],"\\cup":[16],"\\{":[17],"\\Delta":[18,22],"\\}":[19],",":[20],"where":[21,92],"is":[23,53,70,112,123],"an":[24],"absorbing":[25],"(cemetery),":[27],"and":[28,47,89],"action":[31],"A.":[33],"We":[34],"the":[36,48,93,99,117],"of":[38,128],"finite":[39,66],"occupation":[40,60,68,103,135],"measures":[41,104,136],"restricted":[42],"on":[43],"\\times":[45],"A":[46],"extreme":[49,67],"points":[50],"in":[51],"it.It":[52],"possible":[54],"that":[55,64],"some":[56],"strategies":[57,100],"have":[58],"infinite":[59,102],"measures.Nevertheless,":[61],"prove":[63],"every":[65],"measure":[69],"generated":[71,137],"by":[72,125,138],"deterministic":[74,139],"stationary":[75,140],"strategy.Then,":[76],"for":[77],"MDP,":[79],"constrained":[83,121],"problem":[84],"total":[86],"undiscounted":[87],"criteria":[88],"J":[90,132],"constraints,":[91],"cost":[94],"functions":[95],"are":[96,105],"nonnegative.By":[97],"assumption,":[98],"inducing":[101],"not":[106],"optimal.Then":[107],"our":[108],"second":[109],"main":[110],"result":[111],"that,":[113],"under":[114],"mild":[115],"conditions,":[116],"solution":[118],"to":[119],"MDP":[122],"given":[124],"mixture":[127],"no":[129],"more":[130],"than":[131],"+":[133],"1":[134],"strategies.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-10-10T00:00:00"}