{"id":"https://openalex.org/W3022720367","doi":"https://doi.org/10.5555/1577069.1755841","title":"Learning Permutations with Exponential Weights","display_name":"Learning Permutations with Exponential Weights","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W3022720367","doi":"https://doi.org/10.5555/1577069.1755841","mag":"3022720367"},"language":"en","primary_location":{"id":"mag:3022720367","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/jmlr/jmlr10.html#HelmboldW09","pdf_url":null,"source":{"id":"https://openalex.org/S118988714","display_name":"Journal of Machine Learning Research","issn_l":"1532-4435","issn":["1532-4435","1533-7928"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Journal of Machine Learning Research","raw_type":null},"type":"article","indexed_in":[],"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/A5014740431","display_name":"David P. Helmbold","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David P. Helmbold","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108549518","display_name":"Manfred K. Warmuth","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Manfred K. Warmuth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.4287,"has_fulltext":false,"cited_by_count":84,"citation_normalized_percentile":{"value":0.98191955,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"10","issue":"58","first_page":"1705","last_page":"1736"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9990000128746033,"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":0.993399977684021,"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":0.7805584669113159},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6347252726554871},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6322444677352905},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5958517789840698},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5262583494186401},{"id":"https://openalex.org/keywords/permutation-matrix","display_name":"Permutation matrix","score":0.5187035202980042},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.46004796028137207},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4543655216693878},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4386095404624939},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4185170531272888},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41814830899238586},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39386236667633057},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3005428910255432},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07456621527671814}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.7805584669113159},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6347252726554871},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6322444677352905},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5958517789840698},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5262583494186401},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.5187035202980042},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.46004796028137207},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4543655216693878},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4386095404624939},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4185170531272888},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41814830899238586},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39386236667633057},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3005428910255432},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07456621527671814},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:3022720367","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/jmlr/jmlr10.html#HelmboldW09","pdf_url":null,"source":{"id":"https://openalex.org/S118988714","display_name":"Journal of Machine Learning Research","issn_l":"1532-4435","issn":["1532-4435","1533-7928"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Journal of Machine Learning Research","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W3396763","https://openalex.org/W1495813543","https://openalex.org/W1506313179","https://openalex.org/W1570963478","https://openalex.org/W1598420512","https://openalex.org/W1608316568","https://openalex.org/W1628829797","https://openalex.org/W1724735345","https://openalex.org/W1970041563","https://openalex.org/W1979675141","https://openalex.org/W1984958640","https://openalex.org/W1988790447","https://openalex.org/W1990283121","https://openalex.org/W2010997912","https://openalex.org/W2033468335","https://openalex.org/W2034025033","https://openalex.org/W2059774588","https://openalex.org/W2069317438","https://openalex.org/W2077902449","https://openalex.org/W2093825590","https://openalex.org/W2099811697","https://openalex.org/W2103589858","https://openalex.org/W2115193820","https://openalex.org/W2119883797","https://openalex.org/W2123959253","https://openalex.org/W2131867500","https://openalex.org/W2141996170","https://openalex.org/W2150864256","https://openalex.org/W2161611531","https://openalex.org/W2169401877","https://openalex.org/W2333315597","https://openalex.org/W2610680804","https://openalex.org/W2611627047","https://openalex.org/W2798707604","https://openalex.org/W3023115439","https://openalex.org/W3137830407"],"related_works":["https://openalex.org/W2169401877","https://openalex.org/W1988790447","https://openalex.org/W2137905700","https://openalex.org/W1570963478","https://openalex.org/W2914156981","https://openalex.org/W2333315597","https://openalex.org/W2148825261","https://openalex.org/W2093825590","https://openalex.org/W3023115439","https://openalex.org/W2120745256","https://openalex.org/W2296319761","https://openalex.org/W1970041563","https://openalex.org/W2077902449","https://openalex.org/W2122422466","https://openalex.org/W2152898676","https://openalex.org/W2138637686","https://openalex.org/W2069317438","https://openalex.org/W1575658237","https://openalex.org/W159752407","https://openalex.org/W1508384000"],"abstract_inverted_index":{"We":[0],"give":[1],"an":[2,29,58,88,133],"algorithm":[3,11,121],"for":[4,32],"the":[5,16,34,50,69,97,118,123],"on-line":[6],"learning":[7],"of":[8,41,71,99,110,127],"permutations.":[9,42],"The":[10,43],"maintains":[12],"its":[13],"uncertainty":[14],"about":[15],"target":[17],"permutation":[18,131],"as":[19,132],"a":[20,38,77,80],"doubly":[21],"stochastic":[22],"weight":[23,35,44],"matrix,":[24],"and":[25,57,113],"makes":[26],"predictions":[27],"using":[28],"efficient":[30,116],"method":[31,126],"decomposing":[33],"matrix":[36,45,52],"into":[37],"convex":[39],"combination":[40],"is":[46,61,105],"updated":[47],"by":[48,54],"multiplying":[49],"current":[51],"entries":[53],"exponential":[55],"factors,":[56],"iterative":[59],"procedure":[60,73],"needed":[62],"to":[63,86,91],"restore":[64],"double":[65],"stochasticity.":[66],"Even":[67],"though":[68],"result":[70],"this":[72],"does":[74],"not":[75],"have":[76],"closed":[78],"form,":[79],"new":[81],"analysis":[82],"approach":[83],"allows":[84],"us":[85],"prove":[87],"optimal":[89],"(up":[90],"small":[92],"constant":[93],"factors)":[94],"bound":[95,104],"on":[96],"regret":[98,103],"our":[100],"algorithm.":[101],"This":[102],"significantly":[106],"better":[107],"than":[108],"that":[109],"either":[111],"Kalai":[112],"Vempala's":[114],"more":[115],"Follow":[117],"Perturbed":[119],"Leader":[120],"or":[122],"computationally":[124],"expensive":[125],"explicitly":[128],"representing":[129],"each":[130],"expert.":[134]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":7}],"updated_date":"2025-10-10T17:16:08.811792","created_date":"2025-10-10T00:00:00"}
