{"id":"https://openalex.org/W7203747924","doi":"https://doi.org/10.48550/arxiv.2608.17573","title":"Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and Tight Coordinatewise Rates","display_name":"Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and Tight Coordinatewise Rates","publication_year":2026,"publication_date":"2026-08-18","ids":{"openalex":"https://openalex.org/W7203747924","doi":"https://doi.org/10.48550/arxiv.2608.17573"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.17573","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.17573","pdf_url":"https://arxiv.org/pdf/2608.17573","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","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/2608.17573","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019772382","display_name":"Huibo Xu","orcid":"https://orcid.org/0009-0002-8093-6193","observed_orcids":["https://orcid.org/0009-0002-8093-6193"]},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Xu, Huibo","raw_affiliation_strings":["Nanyang Technological University , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanyang Technological University , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147453294","display_name":"Shi Fu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Fu, Shi","raw_affiliation_strings":["Nanyang Technological University , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanyang Technological University , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079418618","display_name":"Qixin Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Zhang, Qixin","raw_affiliation_strings":["Nanyang Technological University , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanyang Technological University , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074103823","display_name":"Dacheng Tao","orcid":"https://orcid.org/0000-0001-7225-5449","observed_orcids":["https://orcid.org/0000-0001-7225-5449","https://orcid.org/0000-0002-5979-578X","https://orcid.org/0000-0002-9209-036X"]},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Tao, Dacheng","raw_affiliation_strings":["Nanyang Technological University , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanyang Technological University , Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I172675005"],"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":0.9965999722480774,"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":0.9965999722480774,"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/T10136","display_name":"Statistical Methods and Inference","score":0.002099999925121665,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.00019999999494757503,"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/ridge-regression","display_name":"ridge regression","score":0.703000009059906}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.7702000141143799},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.7662000060081482},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6973999738693237},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.48980000615119934},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.40549999475479126},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4036000072956085},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4023999869823456},{"id":"https://openalex.org/C81444415","wikidata":"https://www.wikidata.org/wiki/Q7243535","display_name":"Priming (agriculture)","level":3,"score":0.36059999465942383},{"id":"https://openalex.org/C2776543023","wikidata":"https://www.wikidata.org/wiki/Q2147046","display_name":"Rework","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33390000462532043},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.3255999982357025},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.32260000705718994},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.30550000071525574},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.274399995803833},{"id":"https://openalex.org/C32277403","wikidata":"https://www.wikidata.org/wiki/Q740445","display_name":"Ridge","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.17573","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.17573","pdf_url":"https://arxiv.org/pdf/2608.17573","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.17573","doi":"https://doi.org/10.48550/arxiv.2608.17573","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.17573","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-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.17573","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.17573","pdf_url":"https://arxiv.org/pdf/2608.17573","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203747924.pdf","grobid_xml":"https://content.openalex.org/works/W7203747924.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W403935824","https://openalex.org/W1506313179","https://openalex.org/W1968444040","https://openalex.org/W2119883478","https://openalex.org/W2139716865","https://openalex.org/W2168745297","https://openalex.org/W2493662897","https://openalex.org/W4392544739","https://openalex.org/W4405655184","https://openalex.org/W4408928873"],"related_works":["https://openalex.org/W2106668116","https://openalex.org/W2293665969","https://openalex.org/W7221172463","https://openalex.org/W3099809348","https://openalex.org/W7096016759","https://openalex.org/W2625774898","https://openalex.org/W2806090638","https://openalex.org/W4407308876","https://openalex.org/W2770008080","https://openalex.org/W1997378987"],"abstract_inverted_index":{"In":[0],"high-dimensional":[1],"online":[2,54],"prediction,":[3],"sparse":[4],"comparators":[5],"motivate":[6],"regret":[7,55,118,143,190],"bounds":[8,67,217],"that":[9,68],"depend":[10],"on":[11,225],"sparsity":[12],"rather":[13],"than":[14],"ambient":[15],"dimension.":[16,157],"Feature":[17],"priming":[18,50,176,194],"seeks":[19],"such":[20],"adaptation":[21],"by":[22],"reweighting":[23],"features":[24],"using":[25],"past":[26],"data":[27],"and":[28,37,101,150,172,181],"refitting":[29],"a":[30,102,127,210],"minimum-norm":[31],"predictor.":[32],"At":[33],"COLT":[34],"2023,":[35],"Warmuth":[36],"Amid":[38],"posed":[39],"the":[40,45,58,70,86,93,122,232],"open":[41],"problem":[42],"of":[43,85,121],"whether":[44],"univariate,":[46],"Pearson,":[47],"or":[48],"multivariate":[49,193,238],"rules":[51,125,149],"admit":[52],"competitive":[53],"guarantees.":[56],"Under":[57],"natural":[59],"past-only":[60],"Moore--Penrose":[61],"protocol,":[62],"we":[63],"establish":[64],"sparse-regret":[65],"lower":[66,200,216],"refute":[69],"corresponding":[71],"sparse-logarithmic":[72],"guarantee.":[73],"The":[74,198,236],"key":[75],"obstruction":[76,107],"is":[77,162],"cheap":[78],"nuisance":[79],"interpolation,":[80],"which":[81],"permits":[82],"exact":[83,98,237],"interpolation":[84],"history":[87],"while":[88,209],"assigning":[89],"insufficient":[90],"weight":[91],"to":[92],"truly":[94],"predictive":[95],"coordinate.":[96],"An":[97],"target-mass":[99],"identity":[100],"two-sign":[103],"argument":[104],"convert":[105],"this":[106],"into":[108],"clipped":[109,117],"prediction":[110],"loss.":[111],"Hadamard":[112],"constructions":[113],"yield":[114],"$\u03a9(\\min\\{T,\\sqrt":[115],"d\\})$":[116],"for":[119,145,164,173,191,218],"each":[120],"three":[123,147,220],"unit-power":[124,174,192],"against":[126],"zero-loss":[128],"one-sparse":[129],"comparator.":[130],"For":[131],"every":[132],"fixed":[133],"power":[134],"$\u03b1\\ge1$,":[135],"one":[136],"shared":[137],"paired":[138,211],"construction":[139,187,213],"further":[140],"yields":[141,214],"linear":[142,215],"simultaneously":[144],"all":[146,219],"powered":[148,165,221],"selectors":[151],"among":[152],"them":[153],"in":[154],"sufficiently":[155],"high":[156],"A":[158,184],"rank":[159],"upper":[160],"bound":[161,201],"tight":[163],"univariate":[166,199],"priming,":[167],"even":[168],"with":[169,177,231],"Euclidean-unit":[170,196],"inputs,":[171],"Pearson":[175],"coordinatewise":[178],"bounded":[179],"inputs":[180],"target-preserving":[182],"totalization.":[183],"separate":[185],"algebraic":[186],"gives":[188],"$\u03a9(\\min\\{T,d^{1/4}\\})$":[189],"under":[195,203],"inputs.":[197],"persists":[202],"any":[204],"nonnegative":[205],"second-stage":[206],"ridge":[207,212],"schedule,":[208],"rules.":[222],"Exploratory":[223],"diagnostics":[224],"frozen":[226],"language-model":[227],"activations":[228],"are":[229],"consistent":[230],"same":[233],"qualitative":[234],"mechanism.":[235],"frontier":[239],"remains":[240],"open.":[241]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-20T00:00:00"}
