{"id":"https://openalex.org/W1984332158","doi":"https://doi.org/10.1109/tit.2013.2277869","title":"Bandits With Heavy Tail","display_name":"Bandits With Heavy Tail","publication_year":2013,"publication_date":"2013-08-08","ids":{"openalex":"https://openalex.org/W1984332158","doi":"https://doi.org/10.1109/tit.2013.2277869","mag":"1984332158"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2013.2277869","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2277869","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/A5021842384","display_name":"S\u00e9bastien Bubeck","orcid":"https://orcid.org/0000-0001-9122-4410"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sebastien Bubeck","raw_affiliation_strings":["Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ, USA","Dept. of Oper. Res. & Financial Eng., Princeton Univ., Princeton, NJ, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Dept. of Oper. Res. & Financial Eng., Princeton Univ., Princeton, NJ, USA#TAB#","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074621968","display_name":"Nicol\u00f2 Cesa\u2010Bianchi","orcid":"https://orcid.org/0000-0001-8477-4748"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Nicolo Cesa-Bianchi","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e1 degli Studi di Milano, Milano, Italy","Dipt. di Inf., Univ. degli Studi di Milano, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e1 degli Studi di Milano, Milano, Italy","institution_ids":["https://openalex.org/I189158943"]},{"raw_affiliation_string":"Dipt. di Inf., Univ. degli Studi di Milano, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034680608","display_name":"G\u00e1bor Lugosi","orcid":"https://orcid.org/0000-0003-1614-5901"},"institutions":[{"id":"https://openalex.org/I11932220","display_name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats","ror":"https://ror.org/0371hy230","country_code":"ES","type":"nonprofit","lineage":["https://openalex.org/I11932220"]},{"id":"https://openalex.org/I170486558","display_name":"Pompeu Fabra University","ror":"https://ror.org/04n0g0b29","country_code":"ES","type":"education","lineage":["https://openalex.org/I170486558"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Gabor Lugosi","raw_affiliation_strings":["Department of Economics, ICREA and Universitat Pompeu Fabra, Barcelona, Spain","Dept. of Econ., Univ. Pompeu Fabra, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Economics, ICREA and Universitat Pompeu Fabra, Barcelona, Spain","institution_ids":["https://openalex.org/I170486558","https://openalex.org/I11932220"]},{"raw_affiliation_string":"Dept. of Econ., Univ. Pompeu Fabra, Barcelona, Spain","institution_ids":["https://openalex.org/I170486558"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021842384"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":10.6644,"has_fulltext":false,"cited_by_count":249,"citation_normalized_percentile":{"value":0.98341605,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"59","issue":"11","first_page":"7711","last_page":"7717"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9976999759674072,"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/T12288","display_name":"Optimization and Search Problems","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/regret","display_name":"Regret","score":0.7214564085006714},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7203809022903442},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.7004767656326294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5191104412078857},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.47945037484169006},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.44517359137535095},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.42019200325012207},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41998618841171265},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4170539975166321},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41692090034484863},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3826923668384552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3584989011287689},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3217790126800537},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.29754766821861267},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.09000205993652344}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.7214564085006714},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7203809022903442},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7004767656326294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5191104412078857},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.47945037484169006},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.44517359137535095},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.42019200325012207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41998618841171265},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4170539975166321},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41692090034484863},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3826923668384552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3584989011287689},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3217790126800537},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.29754766821861267},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.09000205993652344},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2013.2277869","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2277869","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W638603679","https://openalex.org/W1501823362","https://openalex.org/W1505731132","https://openalex.org/W1517928879","https://openalex.org/W1585839838","https://openalex.org/W1972837134","https://openalex.org/W1983691438","https://openalex.org/W1998498767","https://openalex.org/W2000080679","https://openalex.org/W2002232182","https://openalex.org/W2009551863","https://openalex.org/W2022090913","https://openalex.org/W2046033161","https://openalex.org/W2049934117","https://openalex.org/W2071884978","https://openalex.org/W2080745194","https://openalex.org/W2095709533","https://openalex.org/W2114909350","https://openalex.org/W2168405694","https://openalex.org/W2489822048","https://openalex.org/W2962748815","https://openalex.org/W2963750583","https://openalex.org/W3106395004","https://openalex.org/W4232158517","https://openalex.org/W4242941051","https://openalex.org/W6630117878"],"related_works":["https://openalex.org/W2971351794","https://openalex.org/W4376155396","https://openalex.org/W1947085858","https://openalex.org/W2101991911","https://openalex.org/W2174986909","https://openalex.org/W2527791220","https://openalex.org/W3122602933","https://openalex.org/W2950038056","https://openalex.org/W1544940847","https://openalex.org/W2289285490"],"abstract_inverted_index":{"The":[0],"stochastic":[1],"multiarmed":[2],"bandit":[3,20],"problem":[4,21],"is":[5],"well":[6],"understood":[7],"when":[8,126],"the":[9,19,23,27,68,91,95,108,121],"reward":[10,74],"distributions":[11,28],"are":[12,61],"sub-Gaussian.":[13],"In":[14,76],"this":[15],"paper,":[16],"we":[17,82],"examine":[18],"under":[22,72],"weaker":[24],"assumption":[25],"that":[26,117,120],"have":[29],"moments":[30,54],"of":[31,55,67,90],"order":[32,56,70,77],"<formula":[33,44,100,127],"formulatype=\"inline\"":[34,45,101,128],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[35,46,102,129],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[36,47,103],"Notation=\"TeX\">$1":[37],"+":[38],"\\varepsilon":[39,49,133],"$</tex></formula>":[40],",":[41],"for":[42],"some":[43],"Notation=\"TeX\">$":[48,132],"\\in":[50],"(0,1]$</tex></formula>":[51],".":[52,136],"Surprisingly,":[53],"2":[57],"(i.e.,":[58],"finite":[59],"variance)":[60],"sufficient":[62],"to":[63,78],"obtain":[64],"regret":[65,124],"bounds":[66,116],"same":[69],"as":[71,94],"sub-Gaussian":[73],"distributions.":[75],"achieve":[79],"such":[80,93],"regret,":[81],"define":[83],"sampling":[84],"strategies":[85],"based":[86],"on":[87],"refined":[88],"estimators":[89],"mean":[92],"truncated":[96],"empirical":[97],"mean,":[98],"Catoni's":[99],"Notation=\"TeX\">$M$</tex>":[104],"</formula>":[105],"-estimator,":[106],"and":[107],"median-of-means":[109],"estimator.":[110],"We":[111],"also":[112,118],"derive":[113],"matching":[114],"lower":[115],"show":[119],"best":[122],"achievable":[123],"deteriorates":[125],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[130],"<tex":[131],"&lt;":[134],"1$</tex></formula>":[135]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":22},{"year":2021,"cited_by_count":29},{"year":2020,"cited_by_count":74},{"year":2019,"cited_by_count":31},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
