{"id":"https://openalex.org/W7164367905","doi":"https://doi.org/10.48550/arxiv.2606.11968","title":"Efficient Multinomial Logistic Bandit via Frequent Directions","display_name":"Efficient Multinomial Logistic Bandit via Frequent Directions","publication_year":2026,"publication_date":"2026-06-10","ids":{"openalex":"https://openalex.org/W7164367905","doi":"https://doi.org/10.48550/arxiv.2606.11968"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.11968","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.11968","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.11968","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012189898","display_name":"Linzhe He","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Linzhe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138432859","display_name":"Yu-Jie Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Yu-Jie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138462658","display_name":"Sifan Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Sifan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138480399","display_name":"Lijun Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Lijun","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":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9936000108718872,"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":0.9936000108718872,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.0027000000700354576,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/regret","display_name":"Regret","score":0.8762999773025513},{"id":"https://openalex.org/keywords/multinomial-logistic-regression","display_name":"Multinomial logistic regression","score":0.6123999953269958},{"id":"https://openalex.org/keywords/multinomial-distribution","display_name":"Multinomial distribution","score":0.5386999845504761},{"id":"https://openalex.org/keywords/sketch","display_name":"Sketch","score":0.5228999853134155},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.5041000247001648},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4758000075817108},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.46129998564720154},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4036000072956085}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.8762999773025513},{"id":"https://openalex.org/C117568660","wikidata":"https://www.wikidata.org/wiki/Q1650843","display_name":"Multinomial logistic regression","level":2,"score":0.6123999953269958},{"id":"https://openalex.org/C192065140","wikidata":"https://www.wikidata.org/wiki/Q1147928","display_name":"Multinomial distribution","level":2,"score":0.5386999845504761},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.538100004196167},{"id":"https://openalex.org/C2779231336","wikidata":"https://www.wikidata.org/wiki/Q7534724","display_name":"Sketch","level":2,"score":0.5228999853134155},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.5041000247001648},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.491100013256073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49079999327659607},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4758000075817108},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46129998564720154},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4036000072956085},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3483999967575073},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.3483999967575073},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33309999108314514},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3125999867916107},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.30959999561309814},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.272599995136261},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26440000534057617},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.25760000944137573}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.11968","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.11968","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.11968","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.11968","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,117],"paper":[1],"studies":[2],"efficient":[3],"online":[4,88],"algorithms":[5],"for":[6],"multinomial":[7,20],"logistic":[8,21],"bandits":[9],"(MLogB),":[10],"where":[11,128,144],"the":[12,84,101,133,145,153,158,162,167,177],"feedback":[13],"distribution":[14],"over":[15],"$K+1$":[16],"outcomes":[17],"follows":[18],"a":[19,33,79,139],"model":[22],"of":[23,36,83,142,157,173],"$d$-dimensional":[24],"action":[25],"vectors.":[26],"A":[27],"representative":[28],"UCB-type":[29],"algorithm,":[30],"OFUL-MLogB,":[31],"achieves":[32],"regret":[34,140,168],"bound":[35,141],"$\\tilde{\\mathcal{O}}(Kd\\sqrt{T})$,":[37],"but":[38],"still":[39],"requires":[40],"$\\mathcal{O}(K^3d^3)$":[41],"time":[42,121],"and":[43,52,94,110,124,180],"$\\mathcal{O}(K^2d^2)$":[44],"space":[45,125],"per":[46],"round":[47],"due":[48],"to":[49,106,171],"parameter":[50,92],"estimation":[51,93],"optimistic":[53],"reward":[54,102],"construction,":[55],"which":[56,69],"is":[57,132,150,164,169],"prohibitive":[58],"in":[59,91,100],"high-dimensional":[60],"settings.":[61],"To":[62],"address":[63],"this":[64],"limitation,":[65],"we":[66],"propose":[67],"EOFD-MLogB,":[68],"integrates":[70],"frequent":[71],"directions":[72],"matrix":[73],"sketching":[74,146],"into":[75],"OFUL-MLogB.":[76,174],"By":[77],"maintaining":[78],"low-rank":[80],"SVD":[81],"sketch":[82,134],"accumulated":[85],"Hessian,":[86],"constrained":[87],"Newton":[89],"updates":[90],"$Kd":[95],"\\times":[96,112],"K$":[97,113],"spectral-norm":[98],"computations":[99],"bonus":[103],"are":[104],"reduced":[105],"one-dimensional":[107],"root-finding":[108],"tasks":[109],"$K":[111],"eigenvalue":[114],"computations,":[115],"respectively.":[116],"yields":[118],"dominant":[119],"per-round":[120],"complexity":[122,126],"$\\mathcal{O}(Kd(m+K)^2)$":[123],"$\\mathcal{O}(Kd(m+K))$,":[127],"$m":[129],"\\ll":[130],"d$":[131],"size.":[135],"We":[136],"further":[137],"prove":[138],"$\\tilde{\\mathcal{O}}(\u0394_T(Kd\\ln\u0394_T+m)\\sqrt{T})$,":[143],"error":[147],"factor":[148],"$\u0394_T$":[149],"controlled":[151],"by":[152],"$m$-truncated":[154],"spectral":[155],"tail":[156],"Hessian.":[159],"Thus,":[160],"when":[161],"Hessian":[163],"approximately":[165],"low-rank,":[166],"close":[170],"that":[172],"Experiments":[175],"validate":[176],"computational":[178],"efficiency":[179],"competitive":[181],"performance.":[182]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-12T00:00:00"}