{"id":"https://openalex.org/W4391019747","doi":"https://doi.org/10.1109/cdc49753.2023.10384025","title":"Learning Zero-Sum Linear Quadratic Games with Improved Sample Complexity","display_name":"Learning Zero-Sum Linear Quadratic Games with Improved Sample Complexity","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4391019747","doi":"https://doi.org/10.1109/cdc49753.2023.10384025"},"language":"en","primary_location":{"id":"doi:10.1109/cdc49753.2023.10384025","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10384025","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5112998635","display_name":"Jiduan Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Jiduan Wu","raw_affiliation_strings":["ETH Zurich,Department of Computer Science,Switzerland","Department of Computer Science, ETH Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich,Department of Computer Science,Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Department of Computer Science, ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065250840","display_name":"Anas Barakat","orcid":"https://orcid.org/0000-0002-2527-3748"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Anas Barakat","raw_affiliation_strings":["ETH Zurich,Department of Computer Science,Switzerland","Department of Computer Science, ETH Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich,Department of Computer Science,Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Department of Computer Science, ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003899242","display_name":"Ilyas Fatkhullin","orcid":"https://orcid.org/0000-0003-2621-8991"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Ilyas Fatkhullin","raw_affiliation_strings":["ETH Zurich,Department of Computer Science,Switzerland","Department of Computer Science, ETH Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich,Department of Computer Science,Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Department of Computer Science, ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071683073","display_name":"Niao He","orcid":"https://orcid.org/0000-0003-4225-7536"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Niao He","raw_affiliation_strings":["ETH Zurich,Department of Computer Science,Switzerland","Department of Computer Science, ETH Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich,Department of Computer Science,Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Department of Computer Science, ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.3226,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67338793,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"2602","last_page":"2609"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9975000023841858,"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":0.9975000023841858,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9970999956130981,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6007500290870667},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"Sample complexity","score":0.5598604679107666},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.5409366488456726},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5123172998428345},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49650317430496216},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4669175148010254},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4522474706172943},{"id":"https://openalex.org/keywords/zero-sum-game","display_name":"Zero-sum game","score":0.4429616928100586},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43810003995895386},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4134334325790405},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39668038487434387},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.38117435574531555},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32543033361434937},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24453914165496826},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1037198007106781}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6007500290870667},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.5598604679107666},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5409366488456726},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5123172998428345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49650317430496216},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4669175148010254},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4522474706172943},{"id":"https://openalex.org/C136356330","wikidata":"https://www.wikidata.org/wiki/Q156612","display_name":"Zero-sum game","level":3,"score":0.4429616928100586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43810003995895386},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4134334325790405},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39668038487434387},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.38117435574531555},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32543033361434937},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24453914165496826},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1037198007106781},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc49753.2023.10384025","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10384025","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6499999761581421,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G6408426699","display_name":null,"funder_award_id":"200021-207343","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320327714","display_name":"ETH Z\u00fcrich Foundation","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W1574669531","https://openalex.org/W1979381096","https://openalex.org/W1981042292","https://openalex.org/W2004001705","https://openalex.org/W2011866373","https://openalex.org/W2082210980","https://openalex.org/W2115832833","https://openalex.org/W2136379984","https://openalex.org/W2146845454","https://openalex.org/W2256994888","https://openalex.org/W2947577977","https://openalex.org/W2958746411","https://openalex.org/W2972523776","https://openalex.org/W2975981953","https://openalex.org/W2984078320","https://openalex.org/W2995824757","https://openalex.org/W3019868075","https://openalex.org/W3046992251","https://openalex.org/W3166923021","https://openalex.org/W3188363771","https://openalex.org/W3193634099","https://openalex.org/W3203485495","https://openalex.org/W3206480318","https://openalex.org/W3209135762","https://openalex.org/W3212753778","https://openalex.org/W4210265003","https://openalex.org/W4231367092","https://openalex.org/W4235469235","https://openalex.org/W4288093940","https://openalex.org/W4308031363","https://openalex.org/W4310627894","https://openalex.org/W4327670962","https://openalex.org/W4367841446","https://openalex.org/W4388319978","https://openalex.org/W4391019747","https://openalex.org/W6606291809","https://openalex.org/W6651597697","https://openalex.org/W6754297394","https://openalex.org/W6756870468","https://openalex.org/W6762982123","https://openalex.org/W6763496775","https://openalex.org/W6765601489","https://openalex.org/W6768991564","https://openalex.org/W6770404689","https://openalex.org/W6772021581","https://openalex.org/W6782553173","https://openalex.org/W6787869850","https://openalex.org/W6799255795","https://openalex.org/W6846142462","https://openalex.org/W6846749833","https://openalex.org/W6850472282","https://openalex.org/W6850837180"],"related_works":["https://openalex.org/W3011680666","https://openalex.org/W3136378956","https://openalex.org/W4287871712","https://openalex.org/W3006995042","https://openalex.org/W2877093712","https://openalex.org/W2116157560","https://openalex.org/W3004964213","https://openalex.org/W2885522335","https://openalex.org/W4310614650","https://openalex.org/W2128266000"],"abstract_inverted_index":{"Zero-sum":[0],"Linear":[1],"Quadratic":[2],"(LQ)":[3],"games":[4,55],"are":[5],"fundamental":[6],"in":[7,39,103],"optimal":[8],"control":[9,90,215],"and":[10,213],"can":[11],"be":[12],"used":[13],"(i)":[14],"as":[15,27],"a":[16,28,58,149,167,178,189,195,207],"dynamic":[17],"game":[18],"formulation":[19],"for":[20,31,88],"risk-sensitive":[21],"or":[22,25],"robust":[23],"control,":[24],"(ii)":[26],"benchmark":[29],"setting":[30,106],"multi-agent":[32],"reinforcement":[33],"learning":[34],"with":[35,63],"two":[36],"competing":[37],"agents":[38],"continuous":[40],"state-control":[41],"spaces.":[42],"In":[43,144],"contrast":[44],"to":[45,126],"the":[46,95,98,104,108,120,134,139,174,184,217],"well-studied":[47],"single-agent":[48],"linear":[49],"quadratic":[50],"regulator":[51],"problem,":[52],"zero-sum":[53],"LQ":[54],"entail":[56],"solving":[57],"challenging":[59],"nonconvex-nonconcave":[60],"min-max":[61],"problem":[62],"an":[64,76,128],"objective":[65],"function":[66],"that":[67],"lacks":[68],"coercivity.":[69],"Recently,":[70],"Zhang":[71,116],"et":[72,117],"al.":[73,118],"[1]":[74],"discovered":[75],"implicit":[77,141],"regularization":[78,142],"property":[79],"of":[80,97,110,133,161,216],"natural":[81,219],"policy":[82],"gradient":[83,220],"methods":[84],"which":[85],"is":[86,113,186],"crucial":[87],"safety-critical":[89],"systems":[91],"since":[92],"it":[93],"preserves":[94],"robustness":[96],"controller":[99],"during":[100],"learning.":[101],"Moreover,":[102],"model-free":[105],"where":[107],"knowledge":[109],"model":[111],"parameters":[112],"not":[114],"available,":[115],"proposed":[119],"first":[121],"polynomial":[122],"sample":[123,156,171,200],"complexity":[124,157,172],"algorithm":[125,154,211],"reach":[127],"<tex":[129,168,197],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[130,169,198],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\epsilon$</tex>":[131],"neighborhood":[132],"Nash":[135],"equilibrium":[136],"while":[137],"maintaining":[138],"desirable":[140],"property.":[143],"this":[145],"work,":[146],"we":[147],"propose":[148],"simpler":[150],"nested":[151,210],"Zeroth-Order":[152],"(ZO)":[153],"improving":[155],"by":[158,188],"several":[159],"orders":[160],"magnitude.":[162],"Our":[163,202],"main":[164],"result":[165],"guarantees":[166],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\tilde{\\mathcal{O}}(\\epsilon^{-3})$</tex>":[170],"under":[173],"same":[175],"assumptions":[176],"using":[177],"single-point":[179],"ZO":[180,218],"estimator.":[181],"Furthermore,":[182],"when":[183],"estimator":[185],"replaced":[187],"two-point":[190],"estimator,":[191],"our":[192],"method":[193],"enjoys":[194],"better":[196],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\tilde{\\mathcal{O}}(\\epsilon^{-2})$</tex>":[199],"complexity.":[201],"key":[203],"improvements":[204],"rely":[205],"on":[206],"more":[208],"sample-efficient":[209],"design":[212],"finer":[214],"estimation":[221],"error.":[222]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}