{"id":"https://openalex.org/W3110979110","doi":"https://doi.org/10.1109/tnnls.2020.3041469","title":"Online Minimax Q Network Learning for Two-Player Zero-Sum Markov Games","display_name":"Online Minimax Q Network Learning for Two-Player Zero-Sum Markov Games","publication_year":2020,"publication_date":"2020-12-11","ids":{"openalex":"https://openalex.org/W3110979110","doi":"https://doi.org/10.1109/tnnls.2020.3041469","mag":"3110979110","pmid":"https://pubmed.ncbi.nlm.nih.gov/33306474"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2020.3041469","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3041469","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5080193690","display_name":"Yuanheng Zhu","orcid":"https://orcid.org/0000-0001-5384-423X"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"id":"https://openalex.org/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuanheng Zhu","raw_affiliation_strings":["School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China","State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210100255","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210094879","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100624298","display_name":"Dongbin Zhao","orcid":"https://orcid.org/0000-0001-8218-9633"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"id":"https://openalex.org/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongbin Zhao","raw_affiliation_strings":["School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China","State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210100255","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210094879","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080193690"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879","https://openalex.org/I4210100255","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":5.6244,"has_fulltext":false,"cited_by_count":85,"citation_normalized_percentile":{"value":0.9665232,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"33","issue":"3","first_page":"1228","last_page":"1241"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9997000098228455,"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":0.9997000098228455,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9818000197410583,"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/reinforcement-learning","display_name":"Reinforcement learning","score":0.8036949634552002},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.7738977670669556},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7309727072715759},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.7095783948898315},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6931132078170776},{"id":"https://openalex.org/keywords/zero-sum-game","display_name":"Zero-sum game","score":0.6753647327423096},{"id":"https://openalex.org/keywords/q-learning","display_name":"Q-learning","score":0.5808081030845642},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.534538984298706},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5260332226753235},{"id":"https://openalex.org/keywords/markov-perfect-equilibrium","display_name":"Markov perfect equilibrium","score":0.5118824243545532},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4794020652770996},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.4655599892139435},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.4431513547897339},{"id":"https://openalex.org/keywords/fictitious-play","display_name":"Fictitious play","score":0.4389134347438812},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.4329186975955963},{"id":"https://openalex.org/keywords/example-of-a-game-without-a-value","display_name":"Example of a game without a value","score":0.4288651645183563},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4020169973373413},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3161377012729645},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.31358933448791504},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.2699654698371887},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2579583525657654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2490442991256714},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.19536983966827393},{"id":"https://openalex.org/keywords/combinatorial-game-theory","display_name":"Combinatorial game theory","score":0.17538851499557495}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.8036949634552002},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.7738977670669556},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7309727072715759},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7095783948898315},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6931132078170776},{"id":"https://openalex.org/C136356330","wikidata":"https://www.wikidata.org/wiki/Q156612","display_name":"Zero-sum game","level":3,"score":0.6753647327423096},{"id":"https://openalex.org/C188116033","wikidata":"https://www.wikidata.org/wiki/Q2664563","display_name":"Q-learning","level":3,"score":0.5808081030845642},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.534538984298706},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5260332226753235},{"id":"https://openalex.org/C67091656","wikidata":"https://www.wikidata.org/wiki/Q6771328","display_name":"Markov perfect equilibrium","level":3,"score":0.5118824243545532},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4794020652770996},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.4655599892139435},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.4431513547897339},{"id":"https://openalex.org/C145071142","wikidata":"https://www.wikidata.org/wiki/Q1411116","display_name":"Fictitious play","level":3,"score":0.4389134347438812},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.4329186975955963},{"id":"https://openalex.org/C138328387","wikidata":"https://www.wikidata.org/wiki/Q5419308","display_name":"Example of a game without a value","level":5,"score":0.4288651645183563},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4020169973373413},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3161377012729645},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.31358933448791504},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.2699654698371887},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2579583525657654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2490442991256714},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.19536983966827393},{"id":"https://openalex.org/C102234262","wikidata":"https://www.wikidata.org/wiki/Q1320931","display_name":"Combinatorial game theory","level":4,"score":0.17538851499557495},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2020.3041469","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2020.3041469","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:33306474","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33306474","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7099999785423279}],"awards":[{"id":"https://openalex.org/G1594336315","display_name":null,"funder_award_id":"2018AAA0102404","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G2968709009","display_name":null,"funder_award_id":"2018AAA0101005","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1542941925","https://openalex.org/W1680219837","https://openalex.org/W1979239334","https://openalex.org/W2028560736","https://openalex.org/W2052688942","https://openalex.org/W2067050450","https://openalex.org/W2069797667","https://openalex.org/W2109640889","https://openalex.org/W2109912732","https://openalex.org/W2126316555","https://openalex.org/W2131600418","https://openalex.org/W2145339207","https://openalex.org/W2257979135","https://openalex.org/W2321292752","https://openalex.org/W2405379562","https://openalex.org/W2564987128","https://openalex.org/W2567165815","https://openalex.org/W2568214755","https://openalex.org/W2580211036","https://openalex.org/W2581606339","https://openalex.org/W2589677408","https://openalex.org/W2596585349","https://openalex.org/W2746553466","https://openalex.org/W2766447205","https://openalex.org/W2902907165","https://openalex.org/W2942517366","https://openalex.org/W2963890729","https://openalex.org/W2964164283","https://openalex.org/W2974589008","https://openalex.org/W2982316857","https://openalex.org/W4214717370","https://openalex.org/W4233061323","https://openalex.org/W4236158019","https://openalex.org/W4254547512","https://openalex.org/W6600018571","https://openalex.org/W6629379984","https://openalex.org/W6638036514","https://openalex.org/W6677067356","https://openalex.org/W6678835705","https://openalex.org/W6685444567","https://openalex.org/W6696772115","https://openalex.org/W6738796088"],"related_works":["https://openalex.org/W2161697746","https://openalex.org/W3028528379","https://openalex.org/W2395347989","https://openalex.org/W4287644830","https://openalex.org/W4281478226","https://openalex.org/W3092557414","https://openalex.org/W4287125173","https://openalex.org/W3214495026","https://openalex.org/W2971962262","https://openalex.org/W3110979110"],"abstract_inverted_index":{"The":[0,47,112],"Nash":[1,38,127],"equilibrium":[2,39,128],"is":[3,49,90,149,153],"an":[4],"important":[5],"concept":[6],"in":[7],"game":[8,23],"theory.":[9],"It":[10],"describes":[11],"the":[12,37,69,94,109,125,130,135,138,172,175],"least":[13],"exploitability":[14],"of":[15,137,174],"one":[16],"player":[17],"from":[18],"any":[19],"opponents.":[20],"We":[21],"combine":[22],"theory,":[24],"dynamic":[25],"programming,":[26],"and":[27,57,102,133,146],"recent":[28],"deep":[29],"reinforcement":[30],"learning":[31,88,110,140],"(DRL)":[32],"techniques":[33,118],"to":[34,67,76,92,107,123],"online":[35,84,139],"learn":[36],"policy":[40,59],"for":[41,80,129,157,162],"two-player":[42],"zero-sum":[43],"Markov":[44,164],"games":[45],"(TZMGs).":[46],"problem":[48],"first":[50,131],"formulated":[51],"as":[52],"a":[53,63,143],"Bellman":[54],"minimax":[55,85],"equation,":[56],"generalized":[58],"iteration":[60],"(GPI)":[61],"provides":[62],"double-loop":[64],"iterative":[65],"way":[66],"find":[68,124],"equilibrium.":[70],"Then,":[71],"neural":[72],"networks":[73],"are":[74,105,114,119],"introduced":[75],"approximate":[77],"Q":[78,86],"functions":[79],"large-scale":[81],"problems.":[82,166,180],"An":[83],"network":[87,95],"algorithm":[89,141,177],"proposed":[91,176],"train":[93],"with":[96,121,142],"observations.":[97],"Experience":[98],"replay,":[99],"dueling":[100],"network,":[101],"double":[103],"Q-learning":[104],"applied":[106],"improve":[108],"process.":[111],"contributions":[113],"twofold:":[115],"1)":[116],"DRL":[117],"combined":[120],"GPI":[122],"TZMG":[126,179],"time":[132],"2)":[134],"convergence":[136],"lookup":[144],"table":[145],"experience":[147],"replay":[148],"proven,":[150],"whose":[151],"proof":[152],"not":[154],"only":[155],"useful":[156],"TZMGs":[158],"but":[159],"also":[160],"instructive":[161],"single-agent":[163],"decision":[165],"Experiments":[167],"on":[168,178],"different":[169],"examples":[170],"validate":[171],"effectiveness":[173]},"counts_by_year":[{"year":2025,"cited_by_count":21},{"year":2024,"cited_by_count":23},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":10}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}