{"id":"https://openalex.org/W2076202796","doi":"https://doi.org/10.1109/cdc.2010.5717870","title":"Randomized sampling for large zero-sum games","display_name":"Randomized sampling for large zero-sum games","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2076202796","doi":"https://doi.org/10.1109/cdc.2010.5717870","mag":"2076202796"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2010.5717870","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717870","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th 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/A5032061347","display_name":"Shaunak D. Bopardikar","orcid":"https://orcid.org/0000-0002-0813-7867"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shaunak D. Bopardikar","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, USA","Department of Electrical & Computer Engineering, University of California at Santa Barbara, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of California at Santa Barbara, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004790111","display_name":"Alessandro Borri","orcid":"https://orcid.org/0000-0002-6678-048X"},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alessandro Borri","raw_affiliation_strings":["Department of Electrical Engineering, University of L'' Aquila, Italy","Department of Electrical Engineering, University of L'Aquila, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of L'' Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of L'Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065218317","display_name":"Jo\u00e3o P. Hespanha","orcid":"https://orcid.org/0000-0003-2809-4718"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joao P. Hespanha","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, USA","Department of Electrical & Computer Engineering, University of California at Santa Barbara, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of California at Santa Barbara, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060251698","display_name":"Maria Prandini","orcid":"https://orcid.org/0000-0001-7443-4117"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Maria Prandini","raw_affiliation_strings":["Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy","Dipartimento di Elettronica, e Informazione of the Politecnico di Milano, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Dipartimento di Elettronica, e Informazione of the Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061994256","display_name":"Maria Domenica Di Benedetto","orcid":"https://orcid.org/0000-0001-5703-7822"},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Maria D. Di Benedetto","raw_affiliation_strings":["Department of Electrical Engineering, University of Lquila, Italy","Department of Electrical Engineering, University of L'Aquila, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Lquila, Italy","institution_ids":["https://openalex.org/I26415053"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of L'Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5032061347"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":2.0501,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.86794896,"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":"7675","last_page":"7680"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9973999857902527,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9970999956130981,"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/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6029309034347534},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.56859290599823},{"id":"https://openalex.org/keywords/bayesian-game","display_name":"Bayesian game","score":0.5000464916229248},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4933580458164215},{"id":"https://openalex.org/keywords/zero-sum-game","display_name":"Zero-sum game","score":0.479126900434494},{"id":"https://openalex.org/keywords/outcome","display_name":"Outcome (game theory)","score":0.47294923663139343},{"id":"https://openalex.org/keywords/combinatorial-game-theory","display_name":"Combinatorial game theory","score":0.4664532542228699},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.44958969950675964},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4339383840560913},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.414878249168396},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40741515159606934},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.38718175888061523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37742099165916443},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.35733819007873535},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3217197060585022},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.2757077217102051},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25259000062942505},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.17087560892105103}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6029309034347534},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.56859290599823},{"id":"https://openalex.org/C200594392","wikidata":"https://www.wikidata.org/wiki/Q812529","display_name":"Bayesian game","level":4,"score":0.5000464916229248},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4933580458164215},{"id":"https://openalex.org/C136356330","wikidata":"https://www.wikidata.org/wiki/Q156612","display_name":"Zero-sum game","level":3,"score":0.479126900434494},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.47294923663139343},{"id":"https://openalex.org/C102234262","wikidata":"https://www.wikidata.org/wiki/Q1320931","display_name":"Combinatorial game theory","level":4,"score":0.4664532542228699},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.44958969950675964},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4339383840560913},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.414878249168396},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40741515159606934},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38718175888061523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37742099165916443},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.35733819007873535},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3217197060585022},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.2757077217102051},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25259000062942505},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.17087560892105103},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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":4,"locations":[{"id":"doi:10.1109/cdc.2010.5717870","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717870","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.299.444","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.299.444","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ece.ucsb.edu/~hespanha/published/SSPTechReport.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.380.6731","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.380.6731","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ece.ucsb.edu/~hespanha/published/CDC10_0815_FI.pdf","raw_type":"text"},{"id":"pmh:oai:re.public.polimi.it:11311/573392","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/573392","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W87592707","https://openalex.org/W1490895641","https://openalex.org/W1559661475","https://openalex.org/W1833164934","https://openalex.org/W1859458367","https://openalex.org/W1867531623","https://openalex.org/W1968909445","https://openalex.org/W1971483538","https://openalex.org/W1976466849","https://openalex.org/W1987656566","https://openalex.org/W1999732675","https://openalex.org/W2006041100","https://openalex.org/W2023169397","https://openalex.org/W2056629325","https://openalex.org/W2075567596","https://openalex.org/W2076202796","https://openalex.org/W2096999004","https://openalex.org/W2104371886","https://openalex.org/W2122661687","https://openalex.org/W2125107769","https://openalex.org/W2131295967","https://openalex.org/W2144598735","https://openalex.org/W2148603752","https://openalex.org/W2158479468","https://openalex.org/W2167412190","https://openalex.org/W2180359187","https://openalex.org/W2295428206","https://openalex.org/W2908064020","https://openalex.org/W2914923813","https://openalex.org/W3102712431","https://openalex.org/W3177507093","https://openalex.org/W3212877690","https://openalex.org/W4250913065","https://openalex.org/W4285719527","https://openalex.org/W4302033101"],"related_works":["https://openalex.org/W2392755118","https://openalex.org/W2804582172","https://openalex.org/W4210560602","https://openalex.org/W2569966994","https://openalex.org/W4248264387","https://openalex.org/W2039104542","https://openalex.org/W2910530315","https://openalex.org/W3124955087","https://openalex.org/W2102744185","https://openalex.org/W4234963057"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,43,57,73,92,95,115,128,131,135,146,149,165],"solution":[4],"of":[5,94,130,145,148,167],"large":[6,66],"zero-sum":[7],"matrix":[8],"games":[9,158],"using":[10,38],"randomized":[11,39],"methods.":[12],"We":[13,77],"provide":[14,62],"a":[15,19,88,111,121,175],"procedure":[16,104],"by":[17],"which":[18],"player":[20,112],"can":[21,98,133],"compute":[22],"mixed":[23],"policies":[24,31],"that,":[25],"with":[26,159],"high":[27,75],"probability,":[28],"are":[29,53,143],"security":[30,137],"against":[32],"an":[33],"adversary":[34],"that":[35,52,97,178],"is":[36,105],"also":[37],"methods":[40],"to":[41,71,81,157,173],"solve":[42,82,174],"game.":[44],"The":[45,85,102],"computational":[46],"savings":[47],"result":[48],"from":[49,113],"solving":[50],"subgames":[51,68,96],"much":[54,127],"smaller":[55],"than":[56],"original":[58,150],"game":[59,132,151,177],"and":[60,119,152],"we":[61,170],"bounds":[63,142],"on":[64,91,125],"how":[65,126],"these":[67,168],"should":[69],"be":[70,99],"guarantee":[72],"desired":[74],"probability.":[76],"propose":[78],"two":[79],"methodologies":[80],"this":[83],"problem.":[84],"first":[86,116],"provides":[87,120],"game-independent":[89],"bound":[90,118,124],"size":[93,147],"computed":[100],"a-priori.":[101],"second":[103],"useful":[106],"when":[107],"computation":[108],"limitations":[109],"prevent":[110],"satisfying":[114],"a-priori":[117],"high-probability":[122],"a-posteriori":[123],"outcome":[129],"violate":[134],"precomputed":[136],"level.":[138],"All":[139],"our":[140],"probabilistic":[141],"independent":[144],"could,":[153],"in":[154],"fact,":[155],"apply":[156,171],"continuous":[160],"action":[161],"spaces.":[162],"To":[163],"demonstrate":[164],"usefulness":[166],"results,":[169],"them":[172],"hide-and-seek":[176],"exhibits":[179],"exponential":[180],"complexity.":[181]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
