{"id":"https://openalex.org/W2093562354","doi":"https://doi.org/10.1109/tnet.2011.2181864","title":"Combinatorial Network Optimization With Unknown Variables: Multi-Armed Bandits With Linear Rewards and Individual Observations","display_name":"Combinatorial Network Optimization With Unknown Variables: Multi-Armed Bandits With Linear Rewards and Individual Observations","publication_year":2012,"publication_date":"2012-03-09","ids":{"openalex":"https://openalex.org/W2093562354","doi":"https://doi.org/10.1109/tnet.2011.2181864","mag":"2093562354"},"language":"en","primary_location":{"id":"doi:10.1109/tnet.2011.2181864","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnet.2011.2181864","pdf_url":null,"source":{"id":"https://openalex.org/S62238642","display_name":"IEEE/ACM Transactions on Networking","issn_l":"1063-6692","issn":["1063-6692","1558-2566"],"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/ACM Transactions on Networking","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/A5011040174","display_name":"Yi Gai","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yi Gai","raw_affiliation_strings":["Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","Dept. of Electr. Eng. Univ. of Southern California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Dept. of Electr. Eng. Univ. of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063784062","display_name":"Bhaskar Krishnamachari","orcid":"https://orcid.org/0000-0002-9994-9931"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bhaskar Krishnamachari","raw_affiliation_strings":["Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","Dept. of Electr. Eng. Univ. of Southern California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Dept. of Electr. Eng. Univ. of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002082998","display_name":"Rahul Jain","orcid":"https://orcid.org/0000-0003-3786-8682"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rahul Jain","raw_affiliation_strings":["Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","Dept. of Electr. Eng. Univ. of Southern California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Dept. of Electr. Eng. Univ. of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011040174"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":29.3926,"has_fulltext":false,"cited_by_count":433,"citation_normalized_percentile":{"value":0.99804344,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"20","issue":"5","first_page":"1466","last_page":"1478"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":1.0,"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/T12288","display_name":"Optimization and Search Problems","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.994700014591217,"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/regret","display_name":"Regret","score":0.7995725274085999},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.592319130897522},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5727911591529846},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"Combinatorial optimization","score":0.5323111414909363},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5272910594940186},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5211862921714783},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4492102265357971},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4461619555950165},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4339456260204315},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.4160105586051941},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4136938750743866},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38781917095184326},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22035539150238037},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10839557647705078}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.7995725274085999},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.592319130897522},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5727911591529846},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.5323111414909363},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5272910594940186},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5211862921714783},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4492102265357971},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4461619555950165},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4339456260204315},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.4160105586051941},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4136938750743866},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38781917095184326},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22035539150238037},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10839557647705078},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnet.2011.2181864","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnet.2011.2181864","pdf_url":null,"source":{"id":"https://openalex.org/S62238642","display_name":"IEEE/ACM Transactions on Networking","issn_l":"1063-6692","issn":["1063-6692","1558-2566"],"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/ACM Transactions on Networking","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.705.9857","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.705.9857","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-scf.usc.edu/%7Eygai/publications/TON2012.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6200000047683716,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W50486269","https://openalex.org/W1557310162","https://openalex.org/W1812024992","https://openalex.org/W1965680834","https://openalex.org/W1977545325","https://openalex.org/W2000080679","https://openalex.org/W2003809182","https://openalex.org/W2009551863","https://openalex.org/W2010029425","https://openalex.org/W2014482607","https://openalex.org/W2015056750","https://openalex.org/W2017927472","https://openalex.org/W2018994370","https://openalex.org/W2020254732","https://openalex.org/W2023954497","https://openalex.org/W2038263585","https://openalex.org/W2059608229","https://openalex.org/W2061753713","https://openalex.org/W2108114251","https://openalex.org/W2115293355","https://openalex.org/W2120125372","https://openalex.org/W2125724988","https://openalex.org/W2140571193","https://openalex.org/W2145519285","https://openalex.org/W2148250692","https://openalex.org/W2152964475","https://openalex.org/W2158807713","https://openalex.org/W2168405694","https://openalex.org/W2169528473","https://openalex.org/W2169926276","https://openalex.org/W2222512263","https://openalex.org/W2227557434","https://openalex.org/W2338905098","https://openalex.org/W2481108008","https://openalex.org/W2555165072","https://openalex.org/W2616697817","https://openalex.org/W2962764550","https://openalex.org/W2963007414","https://openalex.org/W3103604572","https://openalex.org/W3140805787","https://openalex.org/W4210431029","https://openalex.org/W4232620022","https://openalex.org/W4233756358","https://openalex.org/W4255306344","https://openalex.org/W4285719527","https://openalex.org/W6602031475","https://openalex.org/W6637310442","https://openalex.org/W6654532046","https://openalex.org/W6676576766"],"related_works":["https://openalex.org/W4376155396","https://openalex.org/W2971351794","https://openalex.org/W1947085858","https://openalex.org/W2101991911","https://openalex.org/W2174986909","https://openalex.org/W2527791220","https://openalex.org/W2155070487","https://openalex.org/W2363855676","https://openalex.org/W2145157516","https://openalex.org/W2402031358"],"abstract_inverted_index":{"We":[0,214],"formulate":[1],"the":[2,47,52,74,88,91,99,109,170,174,177,180,190,209,236,251,259],"following":[3],"combinatorial":[4,135],"multi-armed":[5,157],"bandit":[6],"(MAB)":[7],"problem:":[8],"There":[9],"are":[10,20,57,223],"<i":[11],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[12],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</i>":[13],"random":[14,33,55,103],"variables":[15,34,56,70],"with":[16,46,138,159,197,231],"unknown":[17,212,239,254],"mean":[18,100],"that":[19,60,83,97,106,129,222,228,247,286],"each":[21,30,102],"instantiated":[22],"in":[23,127,201,208,235,250],"an":[24,40],"i.i.d.":[25],"fashion":[26],"over":[27],"time.":[28],"At":[29],"time":[31],"multiple":[32,160],"can":[35,130],"be":[36,131,163],"selected,":[37],"subject":[38],"to":[39,79,165,186,225],"arbitrary":[41],"constraint":[42],"on":[43,156,195,280],"weights":[44],"associated":[45],"selected":[48,53,69],"variables.":[49,213,240],"All":[50],"of":[51,67,101,123,169,173,182,192,211,238,253,284],"individual":[54],"observed":[58],"at":[59],"time,":[61,232],"and":[62,105,117,149,204,233],"a":[63,81,95,281,290],"linearly":[64,249],"weighted":[65,145],"combination":[66],"these":[68,242,265],"is":[71,78,114,263,287,294],"yielded":[72],"as":[73,87,133,143],"reward.":[75],"The":[76],"goal":[77],"find":[80],"policy":[82],"minimizes":[84],"regret,":[85,202],"defined":[86],"difference":[89],"between":[90],"reward":[92],"obtained":[93,107],"by":[94,108],"genie":[96],"knows":[98],"variable,":[104],"given":[110],"policy.":[111],"This":[112],"formulation":[113,167],"broadly":[115],"applicable":[116],"useful":[118],"for":[119,189,219],"stochastic":[120],"online":[121],"versions":[122],"many":[124],"interesting":[125],"tasks":[126],"networks":[128],"formulated":[132],"tractable":[134],"optimization":[136],"problems":[137,257],"linear":[139],"objective":[140],"functions,":[141],"such":[142],"maximum":[144],"matching,":[146],"shortest":[147],"path,":[148],"minimum":[150],"spanning":[151],"tree":[152],"computations.":[153],"Prior":[154],"work":[155,194],"bandits":[158],"plays":[161],"cannot":[162],"applied":[164],"this":[166,220],"because":[168],"general":[171],"nature":[172],"constraint.":[175],"On":[176],"other":[178],"hand,":[179],"mapping":[181],"all":[183],"feasible":[184],"combinations":[185],"arms":[187],"allows":[188],"use":[191],"prior":[193],"MAB":[196],"single-play,":[198],"but":[199],"results":[200,279],"storage,":[203],"computation":[205],"growing":[206],"exponentially":[207],"number":[210,237,252],"present":[215,278],"new":[216],"efficient":[217],"policies":[218,243,266],"problem":[221,262],"shown":[224],"achieve":[226],"regret":[227,285],"grows":[229,248],"logarithmically":[230],"polynomially":[234],"Furthermore,":[241],"only":[244,269],"require":[245,268],"storage":[246],"parameters.":[255],"For":[256,272],"where":[258],"underlying":[260],"deterministic":[261],"tractable,":[264],"further":[267],"polynomial":[270],"computation.":[271],"computationally":[273],"intractable":[274],"problems,":[275],"we":[276],"also":[277],"different":[282],"notion":[283],"suitable":[288],"when":[289],"polynomial-time":[291],"approximation":[292],"algorithm":[293],"used.":[295]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":25},{"year":2023,"cited_by_count":27},{"year":2022,"cited_by_count":29},{"year":2021,"cited_by_count":37},{"year":2020,"cited_by_count":96},{"year":2019,"cited_by_count":48},{"year":2018,"cited_by_count":39},{"year":2017,"cited_by_count":17},{"year":2016,"cited_by_count":28},{"year":2015,"cited_by_count":22},{"year":2014,"cited_by_count":20},{"year":2013,"cited_by_count":21},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
