{"id":"https://openalex.org/W7214740723","doi":"https://doi.org/10.48550/arxiv.2609.32478","title":"Agnostic Smoothed Online Regression with Adversarial Responses","display_name":"Agnostic Smoothed Online Regression with Adversarial Responses","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214740723","doi":"https://doi.org/10.48550/arxiv.2609.32478"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32478","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32478","pdf_url":"https://arxiv.org/pdf/2609.32478","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.32478","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153412628","display_name":"Xuanyu Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chen, Xuanyu","raw_affiliation_strings":["Equal contribution. Department of Statistics , University of Michigan ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equal contribution. Department of Statistics , University of Michigan ;","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153541239","display_name":"Yue Yu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yu, Yue","raw_affiliation_strings":["Equal contribution. Department of Statistics , University of Michigan ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equal contribution. Department of Statistics , University of Michigan ;","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9990000128746033,"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":0.9990000128746033,"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":0.00039999998989515007,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.0,"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/sublinear-regret","display_name":"sublinear regret","score":0.7559999823570251},{"id":"https://openalex.org/keywords/pseudo-dimension","display_name":"pseudo-dimension","score":0.8109999895095825},{"id":"https://openalex.org/keywords/minimax-regret","display_name":"minimax regret","score":0.597000002861023},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.703000009059906},{"id":"https://openalex.org/keywords/linear-predictor","display_name":"linear predictor","score":0.7379999756813049},{"id":"https://openalex.org/keywords/empirical-risk-minimization","display_name":"empirical risk minimization","score":0.6899999976158142}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.728600025177002},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6855999827384949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6449000239372253},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6427000164985657},{"id":"https://openalex.org/C119043178","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Covariate","level":2,"score":0.607699990272522},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5767999887466431},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5669000148773193},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.5455999970436096},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4684000015258789},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4584999978542328},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.4316999912261963},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4207000136375427},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3978999853134155},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.38690000772476196},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3066999912261963},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29589998722076416},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2678000032901764},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2563999891281128}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.32478","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32478","pdf_url":"https://arxiv.org/pdf/2609.32478","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.32478","doi":"https://doi.org/10.48550/arxiv.2609.32478","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32478","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.32478","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32478","pdf_url":"https://arxiv.org/pdf/2609.32478","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214740723.pdf","grobid_xml":"https://content.openalex.org/works/W7214740723.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4238284510","https://openalex.org/W4297794440","https://openalex.org/W7160312337","https://openalex.org/W7168238095","https://openalex.org/W7201832364"],"related_works":["https://openalex.org/W4403324105","https://openalex.org/W3130555334","https://openalex.org/W7133207863","https://openalex.org/W7221020936","https://openalex.org/W4414746924","https://openalex.org/W2941337889","https://openalex.org/W4416053774","https://openalex.org/W4221162406","https://openalex.org/W6891792806","https://openalex.org/W7133242929"],"abstract_inverted_index":{"We":[0,37,86,114],"study":[1],"smoothed":[2,110],"online":[3,111],"prediction":[4],"with":[5,53,67],"bounded":[6,54],"adversarial":[7,17],"responses.":[8],"This":[9,94,147],"widely":[10],"studied":[11],"framework":[12],"bridges":[13],"i.i.d.":[14],"sampling":[15],"and":[16,82,161],"covariate":[18,28,92,140],"selection":[19],"through":[20],"a":[21,32,59,68,79,83,116,137,192],"smoothness":[22],"parameter":[23],"$\\textsf{C}_{\\textsf{cov}}$,":[24],"which":[25],"bounds":[26],"conditional":[27],"densities":[29],"relative":[30],"to":[31,73],"fixed,":[33],"unknown":[34],"base":[35],"measure.":[36],"propose":[38],"\\textsc{Hedge-Cover},":[39],"an":[40,96],"information-theoretic":[41],"algorithm":[42,57],"that":[43,70,183],"achieves":[44],"sublinear":[45],"regret":[46,72,107,187],"$\\widetilde{O}(\\sqrt{\\text{Pdim}(\\mathcal{F})":[47],"\\textsf{C}_{\\textsf{cov}}":[48],"T})$":[49],"for":[50,120,191,203],"function":[51,193],"classes":[52],"pseudo-dimension.":[55],"The":[56,126],"aggregates":[58],"carefully":[60],"constructed":[61],"family":[62],"of":[63,76,108,123,129,151,165,195],"experts":[64],"using":[65],"\\textsc{Hedge},":[66],"prior":[69],"links":[71],"the":[74,103,109,121,130,158,163,174,184],"number":[75,89],"disagreements":[77],"between":[78],"consistent":[80],"selector":[81],"target":[84],"function.":[85],"bound":[87,119,132,177,202],"this":[88,206],"by":[90,181],"exploiting":[91],"smoothness.":[93],"answers":[95],"open":[97],"problem":[98],"posed":[99],"in":[100,134],"\\cite{blanchard2025agnostic}":[101],"on":[102,143,208],"minimax":[104,185],"optimal":[105],"adaptive":[106],"regression":[112],"problem.":[113],"establish":[115],"matching":[117],"lower":[118,131,176],"class":[122,194],"linear":[124],"predictors.":[125],"main":[127],"intricacy":[128],"lies":[133],"explicitly":[135],"constructing":[136],"challenging":[138],"sequential":[139],"distribution":[141],"supported":[142],"mutually":[144],"orthogonal":[145],"hyperplanes.":[146],"construction":[148],"may":[149],"be":[150],"independent":[152],"technical":[153],"interest.":[154],"Finally,":[155],"we":[156,172],"revisit":[157],"well-specified":[159],"setting":[160],"quantify":[162],"effect":[164],"response":[166],"noise.":[167],"For":[168],"conditionally":[169],"$\u03bd^2$-subGaussian":[170],"responses,":[171],"extend":[173],"existing":[175],"under":[178],"realizable":[179],"responses":[180],"showing":[182],"expected":[186],"is":[188],"$\u03a9((1\\vee":[189],"\u03bd)\\sqrt{(\\textsf{C}_{\\textsf{cov}}-1)dT})$":[190],"VC":[196],"dimension":[197],"$d$.":[198],"A":[199],"corresponding":[200],"upper":[201],"ERM":[204],"matches":[205],"dependence":[207],"$\u03bd$.":[209]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}