{"id":"https://openalex.org/W3094530921","doi":"https://doi.org/10.1145/3412815.3416888","title":"On Reinforcement Learning for Turn-based Zero-sum Markov Games","display_name":"On Reinforcement Learning for Turn-based Zero-sum Markov Games","publication_year":2020,"publication_date":"2020-10-15","ids":{"openalex":"https://openalex.org/W3094530921","doi":"https://doi.org/10.1145/3412815.3416888","mag":"3094530921"},"language":"en","primary_location":{"id":"doi:10.1145/3412815.3416888","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3412815.3416888","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3412815.3416888","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2020 ACM-IMS on Foundations of Data Science Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3412815.3416888","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029499294","display_name":"Devavrat Shah","orcid":"https://orcid.org/0000-0003-0737-3259"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Devavrat Shah","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074123276","display_name":"Varun Somani","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Varun Somani","raw_affiliation_strings":["Cornell University, Ithaca, NY, USA"],"affiliations":[{"raw_affiliation_string":"Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008882694","display_name":"Qiaomin Xie","orcid":"https://orcid.org/0000-0003-2834-6866"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qiaomin Xie","raw_affiliation_strings":["Cornell University, Ithaca, NY, USA"],"affiliations":[{"raw_affiliation_string":"Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103269037","display_name":"Zhi Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhi Xu","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029499294"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.2651,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.63934327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"139","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9998000264167786,"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":0.9998000264167786,"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/T11031","display_name":"Game Theory and Applications","score":0.9973999857902527,"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"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.866493821144104},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7087746858596802},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.6575231552124023},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.6308608055114746},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.6307433247566223},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5739440321922302},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5216717720031738},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.517108678817749},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5014185905456543},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4765368402004242},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47592073678970337},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.42072904109954834},{"id":"https://openalex.org/keywords/monte-carlo-tree-search","display_name":"Monte Carlo tree search","score":0.4176001250743866},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3391430974006653},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3356223404407501},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.31550484895706177},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27060312032699585},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.0816592276096344},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07693678140640259}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.866493821144104},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7087746858596802},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.6575231552124023},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6308608055114746},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.6307433247566223},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5739440321922302},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5216717720031738},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.517108678817749},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5014185905456543},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4765368402004242},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47592073678970337},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.42072904109954834},{"id":"https://openalex.org/C46149586","wikidata":"https://www.wikidata.org/wiki/Q11785332","display_name":"Monte Carlo tree search","level":3,"score":0.4176001250743866},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3391430974006653},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3356223404407501},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.31550484895706177},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27060312032699585},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0816592276096344},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07693678140640259},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3412815.3416888","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3412815.3416888","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3412815.3416888","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2020 ACM-IMS on Foundations of Data Science Conference","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3412815.3416888","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3412815.3416888","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3412815.3416888","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2020 ACM-IMS on Foundations of Data Science Conference","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3094530921.pdf","grobid_xml":"https://content.openalex.org/works/W3094530921.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W361876","https://openalex.org/W1490782493","https://openalex.org/W1511694993","https://openalex.org/W1512919909","https://openalex.org/W1513468570","https://openalex.org/W1519783625","https://openalex.org/W1542941925","https://openalex.org/W1548889916","https://openalex.org/W1550386171","https://openalex.org/W1788877992","https://openalex.org/W1973039793","https://openalex.org/W2003832486","https://openalex.org/W2030659867","https://openalex.org/W2038845890","https://openalex.org/W2058557460","https://openalex.org/W2092189895","https://openalex.org/W2120846115","https://openalex.org/W2141076336","https://openalex.org/W2161966552","https://openalex.org/W2257979135","https://openalex.org/W2462023919","https://openalex.org/W2575731723","https://openalex.org/W2607662938","https://openalex.org/W2752024324","https://openalex.org/W2766447205","https://openalex.org/W2912099989","https://openalex.org/W2946912408","https://openalex.org/W2950433453","https://openalex.org/W2970884920","https://openalex.org/W3034377861","https://openalex.org/W4211030719","https://openalex.org/W4254547512","https://openalex.org/W4256361765","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2152670157","https://openalex.org/W2386410636","https://openalex.org/W176737593","https://openalex.org/W2808418668","https://openalex.org/W2903299703","https://openalex.org/W2016648086","https://openalex.org/W3105579180","https://openalex.org/W2156021013","https://openalex.org/W4399157305","https://openalex.org/W2807018115"],"abstract_inverted_index":{"We":[0,52],"consider":[1],"the":[2,15,43,110,114],"problem":[3],"of":[4,68,103,113,130],"finding":[5],"Nash":[6,50,104],"equilibrium":[7,105],"for":[8,56,60,75,82,90,134],"two-player":[9],"turn-based":[10],"zero-sum":[11],"games.":[12],"Inspired":[13],"by":[14],"AlphaGo":[16],"Zero":[17],"(AGZ)":[18],"algorithm,":[19],"we":[20,28,93,125],"develop":[21],"a":[22,65,127],"Reinforcement":[23],"Learning":[24],"based":[25],"approach.":[26,63],"Specifically,":[27],"propose":[29],"Explore-Improve-Supervise":[30],"(EIS)":[31],"method":[32,97],"that":[33,95],"combines":[34],"\"exploration\",":[35,76],"\"policy":[36,83],"improvement\"":[37,84],"and":[38,46,58,85,118],"\"supervised":[39,91],"learning\"":[40],"to":[41],"find":[42],"value":[44,101],"function":[45,102],"policy":[47,72],"associated":[48],"with":[49],"equilibrium.":[51],"identify":[53],"sufficient":[54],"conditions":[55],"convergence":[57],"correctness":[59],"such":[61],"an":[62,99],"For":[64],"concrete":[66],"instance":[67],"EIS":[69],"where":[70],"random":[71],"is":[73,80,88,116,121],"used":[74,81,89],"Monte-Carlo":[77],"Tree":[78],"Search":[79],"Nearest":[86],"Neighbors":[87],"learning\",":[92],"establish":[94,126],"this":[96],"finds":[98],"$\\varepsilon$-approximate":[100],"in":[106],"$\\widetildeO(\\varepsilon^-(d+4))$":[107],"steps":[108],"when":[109],"underlying":[111],"state-space":[112],"game":[115],"continuous":[117],"d-dimensional.":[119],"This":[120],"nearly":[122],"optimal":[123],"as":[124],"lower":[128],"bound":[129],"$\\widetilde\u00d8mega":[131],"(\\varepsilon^-(d+2)":[132],")$":[133],"any":[135],"policy.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}