{"id":"https://openalex.org/W7220973716","doi":"https://doi.org/10.48550/arxiv.2610.07623","title":"Explicit Asymptotic Bounds for Sequential Calibration Beyond $T^{2/3}$","display_name":"Explicit Asymptotic Bounds for Sequential Calibration Beyond $T^{2/3}$","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220973716","doi":"https://doi.org/10.48550/arxiv.2610.07623"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07623","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07623","pdf_url":"https://arxiv.org/pdf/2610.07623","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/2610.07623","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157902860","display_name":"Eric Dai","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dai, Eric","raw_affiliation_strings":["Edison Academy Magnet School"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Edison Academy Magnet School","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028759533","display_name":"Maxwell Fishelson","orcid":"https://orcid.org/0009-0008-8461-3459","observed_orcids":["https://orcid.org/0009-0008-8461-3459"]},"institutions":[{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fishelson, Maxwell","raw_affiliation_strings":["Institute for Advanced Study"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study","institution_ids":["https://openalex.org/I40036882"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.9657999873161316,"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":0.9657999873161316,"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":0.010300000198185444,"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/T11031","display_name":"Game Theory and Applications","score":0.004399999976158142,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sequential-calibration","display_name":"sequential calibration","score":0.8579999804496765},{"id":"https://openalex.org/keywords/probabilistic-forecasting","display_name":"probabilistic forecasting","score":0.6499999761581421},{"id":"https://openalex.org/keywords/binary-outcomes","display_name":"binary outcomes","score":0.7680000066757202}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.79830002784729},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6899999976158142},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.666100025177002},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.5523999929428101},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.46720001101493835},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.44359999895095825},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.39480000734329224},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3874000012874603},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.359499990940094},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.34850001335144043},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3416000008583069},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.311599999666214},{"id":"https://openalex.org/C113336015","wikidata":"https://www.wikidata.org/wiki/Q574010","display_name":"Complete information","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27489998936653137},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27320000529289246},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2533999979496002},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07623","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07623","pdf_url":"https://arxiv.org/pdf/2610.07623","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.2610.07623","doi":"https://doi.org/10.48550/arxiv.2610.07623","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07623","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.07623","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07623","pdf_url":"https://arxiv.org/pdf/2610.07623","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/W7220973716.pdf","grobid_xml":"https://content.openalex.org/works/W7220973716.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7168417392"],"related_works":["https://openalex.org/W4411319998","https://openalex.org/W7223082135","https://openalex.org/W7168417392","https://openalex.org/W4391799110","https://openalex.org/W3172199784","https://openalex.org/W2152875601","https://openalex.org/W7096556013","https://openalex.org/W4415154639","https://openalex.org/W4225089647","https://openalex.org/W2182762018"],"abstract_inverted_index":{"Probability":[0],"forecasts":[1],"are":[2],"calibrated":[3],"when":[4],"predicted":[5],"probabilities":[6],"match":[7],"empirical":[8],"outcome":[9],"frequencies:":[10],"among":[11],"events":[12],"assigned":[13],"a":[14,72],"probability":[15],"$p$,":[16],"we'd":[17],"hope":[18],"that":[19,82],"the":[20,31,63,79,84,97,109,122,134],"fraction":[21],"of":[22,33,36,90,111,121,132],"positive":[23],"outcomes":[24],"is":[25],"close":[26],"to":[27,105,115],"$p$.":[28],"We":[29,70,94],"study":[30],"problem":[32],"sequential":[34,141],"forecasting":[35],"binary":[37],"outcomes.":[38],"The":[39],"classical":[40],"$O(T^{2/3})$":[41],"bound":[42,85,131],"on":[43,102],"expected":[44],"cumulative":[45],"$\\ell_1$-calibration":[46],"error":[47],"established":[48],"by":[49,66,107,143],"Foster":[50],"and":[51,92,147],"Vohra":[52],"stood":[53],"for":[54,78,87,140],"over":[55],"two":[56],"decades":[57],"until":[58],"Dagan":[59,112],"et":[60,113],"al.":[61,114],"reduced":[62],"exponent":[64,137],"$2/3$":[65,139],"an":[67,129],"unspecified":[68],"constant.":[69],"establish":[71,128],"new":[73],"two-phase":[74],"recursive":[75],"labeling":[76],"strategy":[77],"sign-preservation-with-reuse":[80,123],"game":[81],"yields":[83],"$O(n^\u03b1t^\u03b2)$":[86],"all":[88],"choices":[89],"space":[91],"time.":[93],"then":[95],"sharpen":[96],"reduction":[98],"from":[99],"upper":[100],"bounds":[101],"sign":[103],"preservation":[104],"calibration":[106],"modifying":[108],"equivalence":[110],"use":[116],"only":[117],"$O(\\log":[118],"T)$":[119],"instances":[120],"game.":[124],"This":[125],"lets":[126],"us":[127],"explicit":[130,136,149],"$O(T^{0.662942288})$,":[133],"first":[135],"below":[138],"calibration,":[142],"combining":[144],"both":[145],"improvements":[146],"choosing":[148],"feasible":[150],"parameters.":[151]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
