{"id":"https://openalex.org/W7151297894","doi":"https://doi.org/10.48550/arxiv.2604.03525","title":"Online learning of smooth functions on $\\mathbb{R}$","display_name":"Online learning of smooth functions on $\\mathbb{R}$","publication_year":2026,"publication_date":"2026-04-04","ids":{"openalex":"https://openalex.org/W7151297894","doi":"https://doi.org/10.48550/arxiv.2604.03525"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.03525","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.03525","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.2604.03525","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016568974","display_name":"Jesse Geneson","orcid":"https://orcid.org/0000-0001-7148-5947"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Geneson, Jesse","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133081772","display_name":"Kuldeep Singh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Singh, Kuldeep","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133107253","display_name":"Alexander Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Alexander","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/T12072","display_name":"Machine Learning and Algorithms","score":0.7563999891281128,"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"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.7563999891281128,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.13650000095367432,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.024000000208616257,"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/adversary","display_name":"Adversary","score":0.699400007724762},{"id":"https://openalex.org/keywords/adversarial-system","display_name":"Adversarial system","score":0.6676999926567078},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6313999891281128},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5795999765396118},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4311000108718872},{"id":"https://openalex.org/keywords/online-learning","display_name":"Online learning","score":0.3725000023841858},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.34439998865127563}],"concepts":[{"id":"https://openalex.org/C41065033","wikidata":"https://www.wikidata.org/wiki/Q2825412","display_name":"Adversary","level":2,"score":0.699400007724762},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.6676999926567078},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6313999891281128},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6186000108718872},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5795999765396118},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.40389999747276306},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39629998803138733},{"id":"https://openalex.org/C2986087404","wikidata":"https://www.wikidata.org/wiki/Q15946010","display_name":"Online learning","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.34439998865127563},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3181000053882599},{"id":"https://openalex.org/C7606001","wikidata":"https://www.wikidata.org/wiki/Q4686702","display_name":"Adversary model","level":3,"score":0.3156999945640564},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C2781011336","wikidata":"https://www.wikidata.org/wiki/Q1465133","display_name":"Time limit","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C145071142","wikidata":"https://www.wikidata.org/wiki/Q1411116","display_name":"Fictitious play","level":3,"score":0.25780001282691956},{"id":"https://openalex.org/C157692150","wikidata":"https://www.wikidata.org/wiki/Q2919848","display_name":"Query optimization","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.03525","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.03525","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.2604.03525","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.03525","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"adversarial":[2],"online":[3],"learning":[4,78],"of":[5,84,106,132],"real-valued":[6],"functions":[7],"on":[8,56,124],"$\\mathbb{R}$.":[9],"In":[10,93,110,136],"each":[11,100],"round":[12,142],"the":[13,25,39,51,82,96,113,119,139],"learner":[14,120],"is":[15,30,121,144],"queried":[16],"at":[17],"$x_t\\in\\mathbb{R}$,":[18],"predicts":[19],"$\\hat":[20],"y_t$,":[21],"and":[22,62],"then":[23],"observes":[24],"true":[26],"value":[27],"$f(x_t)$;":[28],"performance":[29],"measured":[31],"by":[32,71,146],"cumulative":[33],"$p$-loss":[34],"$\\sum_{t\\ge":[35],"1}|\\hat":[36],"y_t-f(x_t)|^p$.":[37],"For":[38],"class":[40],"\\[":[41],"\\mathcal{G}_q=\\Bigl\\{f:\\mathbb{R}\\to\\mathbb{R}\\":[42],"\\text{absolutely":[43],"continuous}:\\":[44],"\\int_{\\mathbb{R}}|f'(x)|^q\\,dx\\le":[45],"1\\Bigr\\},":[46],"\\]":[47],"we":[48,74],"show":[49],"that":[50,80,86],"standard":[52],"model":[53],"becomes":[54],"ill-posed":[55],"$\\mathbb{R}$:":[57],"for":[58],"every":[59],"$p\\ge":[60],"1$":[61],"$q&gt;1$,":[63],"an":[64],"adversary":[65,97,114],"can":[66],"force":[67],"infinite":[68],"loss.":[69],"Motivated":[70],"this":[72],"obstruction,":[73],"analyze":[75],"three":[76],"modified":[77],"scenarios":[79],"limit":[81],"influence":[83],"queries":[85],"are":[87],"far":[88],"from":[89],"previously":[90],"observed":[91],"inputs.":[92],"Scenario":[94,111,137],"1":[95],"must":[98],"choose":[99],"new":[101],"query":[102,116,127],"within":[103,129],"distance":[104,130],"$1$":[105,131],"some":[107],"past":[108,134],"query.":[109,135],"2":[112],"may":[115],"anywhere,":[117],"but":[118],"penalized":[122],"only":[123],"rounds":[125],"whose":[126],"lies":[128],"a":[133,147],"3":[138],"loss":[140],"in":[141],"$t$":[143],"multiplied":[145],"weight":[148],"$g(\\min_{j":[149]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-08T00:00:00"}
