{"id":"https://openalex.org/W7130609113","doi":"https://doi.org/10.48550/arxiv.2602.16236","title":"Online Prediction of Stochastic Sequences with High Probability Regret Bounds","display_name":"Online Prediction of Stochastic Sequences with High Probability Regret Bounds","publication_year":2026,"publication_date":"2026-02-18","ids":{"openalex":"https://openalex.org/W7130609113","doi":"https://doi.org/10.48550/arxiv.2602.16236"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.16236","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126152976","display_name":"Matthias Frey","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frey, Matthias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046301126","display_name":"Jonathan H. Manton","orcid":"https://orcid.org/0000-0002-2441-588X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Manton, Jonathan H.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007978311","display_name":"Jingge Zhu","orcid":"https://orcid.org/0000-0003-0661-601X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Jingge","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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":0.8662999868392944,"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":0.8662999868392944,"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":0.05739999935030937,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.014000000432133675,"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/regret","display_name":"Regret","score":0.7836999893188477},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.6338000297546387},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5695000290870667},{"id":"https://openalex.org/keywords/impossibility","display_name":"Impossibility","score":0.5303000211715698},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4512999951839447},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4372999966144562},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4221000075340271},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.4131999909877777}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.7836999893188477},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6937000155448914},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6338000297546387},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5695000290870667},{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.5303000211715698},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4512999951839447},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4372999966144562},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4221000075340271},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36890000104904175},{"id":"https://openalex.org/C130648207","wikidata":"https://www.wikidata.org/wiki/Q6007562","display_name":"Imprecise probability","level":3,"score":0.3610000014305115},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3449999988079071},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3375000059604645},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27630001306533813},{"id":"https://openalex.org/C28761237","wikidata":"https://www.wikidata.org/wiki/Q7805321","display_name":"Time horizon","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.16236","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.16236","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.16236","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.16236","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"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":[0,50,104],"revisit":[1],"the":[2,19,44,62,67,101,119,127],"classical":[3],"problem":[4],"of":[5,8,69,72,86,100,121,126],"universal":[6,70],"prediction":[7,71],"stochastic":[9,74],"sequences":[10],"with":[11,37,89],"a":[12,57,73,77,83,124],"finite":[13],"time":[14],"horizon":[15],"$T$":[16],"known":[17,97],"to":[18,30,95,117],"learner.":[20],"The":[21],"question":[22],"we":[23],"investigate":[24],"is":[25,28,114],"whether":[26],"it":[27,113],"possible":[29,116],"derive":[31],"vanishing":[32],"regret":[33],"bounds":[34,42,54,99],"that":[35,46,112],"hold":[36,47],"high":[38],"probability,":[39],"complementing":[40],"existing":[41],"from":[43],"literature":[45],"in":[48,123],"expectation.":[49],"propose":[51,106],"such":[52],"high-probability":[53],"which":[55,110],"have":[56],"very":[58],"similar":[59],"form":[60,129],"as":[61,91],"prior":[63,96],"expectation":[64],"bounds.":[65],"For":[66],"case":[68],"process":[75],"over":[76],"countable":[78],"alphabet,":[79],"our":[80],"bound":[81,125],"states":[82],"convergence":[84],"rate":[85],"$\\mathcal{O}(T^{-1/2}":[87],"\u03b4^{-1/2})$":[88],"probability":[90],"least":[92],"$1-\u03b4$":[93],"compared":[94],"in-expectation":[98],"order":[102],"$\\mathcal{O}(T^{-1/2})$.":[103],"also":[105],"an":[107],"impossibility":[108],"result":[109],"proves":[111],"not":[115],"improve":[118],"exponent":[120],"$\u03b4$":[122],"same":[128],"without":[130],"making":[131],"additional":[132],"assumptions.":[133]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-02-20T00:00:00"}
