{"id":"https://openalex.org/W7139934469","doi":"https://doi.org/10.48550/arxiv.2603.18938","title":"Kernel Single-Index Bandits: Estimation, Inference, and Learning","display_name":"Kernel Single-Index Bandits: Estimation, Inference, and Learning","publication_year":2026,"publication_date":"2026-03-19","ids":{"openalex":"https://openalex.org/W7139934469","doi":"https://doi.org/10.48550/arxiv.2603.18938"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.18938","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18938","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"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.2603.18938","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033425711","display_name":"Sakshi Arya","orcid":"https://orcid.org/0000-0002-7828-6569"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arya, Sakshi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103247006","display_name":"Satarupa Bhattacharjee","orcid":"https://orcid.org/0000-0002-5974-574X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bhattacharjee, Satarupa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109582233","display_name":"Bharath K. Sriperumbudur","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sriperumbudur, Bharath K.","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":0.9865999817848206,"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":0.9865999817848206,"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":0.003000000026077032,"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/T10845","display_name":"Advanced Causal Inference Techniques","score":0.0027000000700354576,"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/estimator","display_name":"Estimator","score":0.583299994468689},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.5526999831199646},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.5461999773979187},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.5291000008583069},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.4772999882698059},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"Central limit theorem","score":0.4627000093460083},{"id":"https://openalex.org/keywords/regret","display_name":"Regret","score":0.4404999911785126},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.4269999861717224},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.4034000039100647},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.38269999623298645}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6972000002861023},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.583299994468689},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.5526999831199646},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.5461999773979187},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.4772999882698059},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.4627000093460083},{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.4404999911785126},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4269999861717224},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38359999656677246},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.3734000027179718},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3700999915599823},{"id":"https://openalex.org/C27406209","wikidata":"https://www.wikidata.org/wiki/Q6394203","display_name":"Kernel smoother","level":5,"score":0.3483000099658966},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.34549999237060547},{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.34279999136924744},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33980000019073486},{"id":"https://openalex.org/C95167961","wikidata":"https://www.wikidata.org/wiki/Q4483495","display_name":"Fiducial inference","level":5,"score":0.33090001344680786},{"id":"https://openalex.org/C971699","wikidata":"https://www.wikidata.org/wiki/Q1132714","display_name":"Delta method","level":3,"score":0.3239000141620636},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3066999912261963},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.28369998931884766},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.2768000066280365},{"id":"https://openalex.org/C98385598","wikidata":"https://www.wikidata.org/wiki/Q1339385","display_name":"Empirical distribution function","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2745000123977661},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C167723999","wikidata":"https://www.wikidata.org/wiki/Q3773214","display_name":"Sampling distribution","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C196842392","wikidata":"https://www.wikidata.org/wiki/Q6664277","display_name":"Local asymptotic normality","level":4,"score":0.25290000438690186},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.2526000142097473}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.18938","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18938","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.18938","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18938","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,30,75,118,168],"study":[1],"contextual":[2,205],"bandits":[3],"with":[4,19,89,114,163],"finitely":[5],"many":[6],"actions":[7],"in":[8,34,203],"which":[9,35,145],"the":[10,47,56,61,86,95,123,142],"reward":[11,96],"of":[12,85],"each":[13],"arm":[14],"follows":[15],"a":[16,32,77,135,195],"single-index":[17,124,204],"model":[18],"an":[20,25],"arm-specific":[21],"index":[22,87],"parameter":[23],"and":[24,42,69,133,201],"unknown":[26],"nonparametric":[27],"link":[28],"function.":[29],"consider":[31],"regime":[33],"arms":[36],"correspond":[37],"to":[38],"stable":[39],"decision":[40],"options":[41],"covariates":[43],"evolve":[44],"adaptively":[45,115],"under":[46,126,177],"bandit":[48],"policy.":[49],"This":[50,98],"setting":[51],"creates":[52],"significant":[53],"statistical":[54,190],"challenges:":[55],"sampling":[57],"distribution":[58],"depends":[59],"on":[60,155],"allocation":[62],"rule,":[63],"observations":[64],"are":[65],"dependent":[66],"over":[67],"time,":[68],"inverse-propensity":[70],"weighting":[71],"induces":[72],"variance":[73],"inflation.":[74],"propose":[76],"kernelized":[78],"$\\varepsilon$-greedy":[79],"algorithm":[80],"that":[81,182],"combines":[82],"Stein-based":[83],"estimation":[84],"parameters":[88],"inverse-propensity-weighted":[90],"kernel":[91],"ridge":[92],"regression":[93],"for":[94,112,122,141,158,198],"functions.":[97],"approach":[99],"enables":[100],"flexible":[101],"semiparametric":[102,183],"learning":[103,200],"while":[104],"retaining":[105],"interpretability.":[106],"Our":[107],"analysis":[108,153],"develops":[109],"new":[110],"tools":[111],"inference":[113,202],"collected":[116],"data.":[117],"establish":[119],"asymptotic":[120],"normality":[121],"estimator":[125],"adaptive":[127],"sampling,":[128],"yielding":[129],"valid":[130,148],"confidence":[131,150],"regions,":[132],"derive":[134],"directional":[136],"functional":[137],"central":[138,165],"limit":[139,166],"theorem":[140],"RKHS":[143],"estimator,":[144],"provides":[146],"asymptotically":[147],"pointwise":[149],"intervals.":[151],"The":[152],"relies":[154],"concentration":[156],"bounds":[157],"inverse-weighted":[159],"Gram":[160],"matrices":[161],"together":[162],"martingale":[164],"theorems.":[167],"further":[169],"obtain":[170],"finite-time":[171],"regret":[172],"guarantees,":[173],"including":[174],"$\\tilde{O}(\\sqrt{T})$":[175],"rates":[176],"common-link":[178],"Lipschitz":[179],"conditions,":[180],"showing":[181],"structure":[184],"can":[185],"be":[186],"exploited":[187],"without":[188],"sacrificing":[189],"efficiency.":[191],"These":[192],"results":[193],"provide":[194],"unified":[196],"framework":[197],"simultaneous":[199],"bandits.":[206]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-21T00:00:00"}