{"id":"https://openalex.org/W3003675412","doi":"https://doi.org/10.1109/tac.2020.2970153","title":"Finding the Equilibrium for Continuous Constrained Markov Games Under the Average Criteria","display_name":"Finding the Equilibrium for Continuous Constrained Markov Games Under the Average Criteria","publication_year":2020,"publication_date":"2020-01-28","ids":{"openalex":"https://openalex.org/W3003675412","doi":"https://doi.org/10.1109/tac.2020.2970153","mag":"3003675412"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2020.2970153","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.2970153","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088416755","display_name":"Xiaofeng Jiang","orcid":"https://orcid.org/0000-0001-7595-2397"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaofeng Jiang","raw_affiliation_strings":["Department of Automation, University of Science and Technology of China, Hefei, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045720734","display_name":"Shuangwu Chen","orcid":"https://orcid.org/0000-0003-2817-9738"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuangwu Chen","raw_affiliation_strings":["Department of Automation, University of Science and Technology of China, Hefei, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083577000","display_name":"Jian Yang","orcid":"https://orcid.org/0000-0002-7329-4738"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Yang","raw_affiliation_strings":["Department of Automation, University of Science and Technology of China, Hefei, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020194895","display_name":"Han Hu","orcid":"https://orcid.org/0000-0001-7532-0496"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Han Hu","raw_affiliation_strings":["School of Information and Electronics, Beijing Institute of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Information and Electronics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060421795","display_name":"Zhenliang Zhang","orcid":"https://orcid.org/0000-0003-4450-9987"},"institutions":[{"id":"https://openalex.org/I4210087596","display_name":"Qualcomm (United States)","ror":"https://ror.org/002zrf773","country_code":"US","type":"company","lineage":["https://openalex.org/I4210087596"]},{"id":"https://openalex.org/I1343180700","display_name":"Intel (United States)","ror":"https://ror.org/01ek73717","country_code":"US","type":"company","lineage":["https://openalex.org/I1343180700"]},{"id":"https://openalex.org/I45928872","display_name":"Alibaba Group (China)","ror":"https://ror.org/00k642b80","country_code":"CN","type":"company","lineage":["https://openalex.org/I45928872"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Zhenliang Zhang","raw_affiliation_strings":["Alibaba DAMO Academy, Hangzhou, China","Intel Labs, Qualcomm New Jersey Research Center, Bridgewater Township, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Alibaba DAMO Academy, Hangzhou, China","institution_ids":["https://openalex.org/I45928872"]},{"raw_affiliation_string":"Intel Labs, Qualcomm New Jersey Research Center, Bridgewater Township, NJ, USA","institution_ids":["https://openalex.org/I4210087596","https://openalex.org/I1343180700"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5088416755"],"corresponding_institution_ids":["https://openalex.org/I126520041"],"apc_list":null,"apc_paid":null,"fwci":0.1326,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50831138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"65","issue":"12","first_page":"5399","last_page":"5406"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9994999766349792,"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/T10603","display_name":"Smart Grid Energy Management","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12761","display_name":"Data Stream Mining Techniques","score":0.9794999957084656,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6881928443908691},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5532354116439819},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.5436742305755615},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.531437337398529},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.4958406388759613},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.48629412055015564},{"id":"https://openalex.org/keywords/strategy","display_name":"Strategy","score":0.461570143699646},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.45498529076576233},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.43714243173599243},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.43384233117103577},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3682517409324646},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.3342750668525696},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27785152196884155}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6881928443908691},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5532354116439819},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5436742305755615},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.531437337398529},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.4958406388759613},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.48629412055015564},{"id":"https://openalex.org/C88959737","wikidata":"https://www.wikidata.org/wiki/Q1546627","display_name":"Strategy","level":3,"score":0.461570143699646},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.45498529076576233},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.43714243173599243},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.43384233117103577},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3682517409324646},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.3342750668525696},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27785152196884155},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2020.2970153","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.2970153","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7900000214576721,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1865835052","display_name":null,"funder_award_id":"61971457","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5156508193","display_name":null,"funder_award_id":"61503358","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6392292501","display_name":null,"funder_award_id":"61233003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8561875612","display_name":null,"funder_award_id":"61673360","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1530927473","https://openalex.org/W1603534221","https://openalex.org/W1771410628","https://openalex.org/W1849094143","https://openalex.org/W1966904284","https://openalex.org/W1977277767","https://openalex.org/W2007158182","https://openalex.org/W2055501135","https://openalex.org/W2119717200","https://openalex.org/W2145339207","https://openalex.org/W2147996349","https://openalex.org/W2155027007","https://openalex.org/W2165150801","https://openalex.org/W2172968643","https://openalex.org/W2173248099","https://openalex.org/W2318523670","https://openalex.org/W2484957131","https://openalex.org/W2586741594","https://openalex.org/W2611866857","https://openalex.org/W2736601468","https://openalex.org/W2763798514","https://openalex.org/W2909859782","https://openalex.org/W2963184621","https://openalex.org/W2963395732","https://openalex.org/W3152478022","https://openalex.org/W4214717370","https://openalex.org/W4231009334","https://openalex.org/W4232146222","https://openalex.org/W6627932998","https://openalex.org/W6638018090","https://openalex.org/W6683204974","https://openalex.org/W6684205842","https://openalex.org/W6684921986","https://openalex.org/W6741002519"],"related_works":["https://openalex.org/W1970303738","https://openalex.org/W3121615138","https://openalex.org/W2581115878","https://openalex.org/W2061042586","https://openalex.org/W1975256383","https://openalex.org/W3141427172","https://openalex.org/W2057383904","https://openalex.org/W3152424015","https://openalex.org/W3122291600","https://openalex.org/W2029785513"],"abstract_inverted_index":{"For":[0],"Markov":[1],"game":[2,51],"with":[3],"cost":[4],"constraints":[5],"and":[6,28,39,54,91,158,163],"continuous":[7,83],"actions,":[8],"the":[9,16,24,36,45,50,55,58,67,82,88,92,96,123,126,130,137,140,146,154,171,177],"local":[10,102,106,131,155],"constraint":[11,156],"of":[12,19,47,57,66,129,139,174],"single-decision":[13],"maker":[14],"is":[15,29,72,114,133],"interacted":[17,98],"result":[18,169],"joint":[20],"actions":[21],"taken":[22],"by":[23,32],"other":[25],"decision":[26,142],"makers,":[27],"usually":[30],"eliminated":[31],"imposing":[33],"penalties":[34,48],"on":[35,122,145],"undesired":[37],"states":[38],"policies,":[40],"which":[41],"may":[42],"suffer":[43],"from":[44],"failure":[46],"as":[49],"policy":[52,85,159],"changes":[53],"nonexistence":[56],"mixed":[59,89],"policies.":[60],"In":[61],"this":[62,76],"article,":[63],"a":[64,101,109,164],"framework":[65],"actor-critic":[68],"deep":[69],"neural":[70],"network":[71,80,94],"utilized":[73],"to":[74,86,135],"solve":[75],"problem.":[77],"The":[78,105,149],"actor":[79],"establishes":[81],"pure":[84],"replace":[87],"policy,":[90],"critic":[93],"converts":[95],"global":[97,147],"results":[99],"into":[100,116],"performance":[103],"potential.":[104],"search":[107],"for":[108],"constrained":[110],"equilibrium":[111],"average":[112],"objective":[113],"converted":[115],"an":[117],"unconstrained":[118],"minimax":[119],"optimization.":[120],"Based":[121],"equivalent":[124],"conversion,":[125],"optimality":[127],"function":[128],"action":[132,144],"given":[134],"evaluate":[136],"influence":[138],"single":[141],"maker's":[143],"system.":[148],"proposed":[150],"algorithm":[151],"simultaneously":[152],"iterates":[153],"multiplier":[157],"along":[160],"opposite":[161],"directions,":[162],"typical":[165],"congestion":[166],"control":[167],"numerical":[168],"in":[170],"emerging":[172],"Internet":[173],"Things":[175],"shows":[176],"efficiency.":[178]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
