{"id":"https://openalex.org/W7213513824","doi":"https://doi.org/10.48550/arxiv.2609.18678","title":"Minimax optimality for sequential gradient-free minimization of smooth functions and their derivatives","display_name":"Minimax optimality for sequential gradient-free minimization of smooth functions and their derivatives","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213513824","doi":"https://doi.org/10.48550/arxiv.2609.18678"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18678","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18678","pdf_url":"https://arxiv.org/pdf/2609.18678","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/2609.18678","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152020042","display_name":"Th\u00e9o Paquier","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210094214","display_name":"\u00c9cole Nationale de la Statistique et de l'Analyse de l'Information","ror":"https://ror.org/00k206f19","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210094214","https://openalex.org/I4210108488"]},{"id":"https://openalex.org/I84009706","display_name":"ENSAE Paris","ror":"https://ror.org/01fz7mn40","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210108488","https://openalex.org/I4210145102","https://openalex.org/I84009706"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Paquier, Th\u00e9o","raw_affiliation_strings":["ENSAI, ENSAE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENSAI, ENSAE","institution_ids":["https://openalex.org/I4210094214","https://openalex.org/I84009706"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112866084","display_name":"Alexandre B. Tsybakov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I84009706","display_name":"ENSAE Paris","ror":"https://ror.org/01fz7mn40","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210108488","https://openalex.org/I4210145102","https://openalex.org/I84009706"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Tsybakov, Alexandre B","raw_affiliation_strings":["ENSAE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENSAE","institution_ids":["https://openalex.org/I84009706"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082182482","display_name":"Fran\u00e7ois Portier","orcid":"https://orcid.org/0000-0002-9283-3135","observed_orcids":["https://orcid.org/0000-0002-9283-3135"]},"institutions":[{"id":"https://openalex.org/I4210094214","display_name":"\u00c9cole Nationale de la Statistique et de l'Analyse de l'Information","ror":"https://ror.org/00k206f19","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210094214","https://openalex.org/I4210108488"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Portier, Fran\u00e7ois","raw_affiliation_strings":["ENSAI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENSAI","institution_ids":["https://openalex.org/I4210094214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091901276","display_name":"Mohammadreza Mousavi Kalan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210137396","display_name":"Centre de Recherche en \u00c9conomie et Statistique","ror":"https://ror.org/0449khs19","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I4210108488","https://openalex.org/I4210137396","https://openalex.org/I4210145102","https://openalex.org/I4210150854","https://openalex.org/I84009706"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Kalan, Mohammadreza M","raw_affiliation_strings":["ENSAI, CREST, CREST"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENSAI, CREST, CREST","institution_ids":["https://openalex.org/I4210137396"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":0.9804999828338623,"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":0.9804999828338623,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.003700000001117587,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.002099999925121665,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/minimax-regret","display_name":"minimax regret","score":0.5740000009536743},{"id":"https://openalex.org/keywords/derivative-free-optimization","display_name":"derivative-free optimization","score":0.7919999957084656},{"id":"https://openalex.org/keywords/noisy-optimization","display_name":"noisy optimization","score":0.6190000176429749},{"id":"https://openalex.org/keywords/holder-functions","display_name":"H\u00f6lder functions","score":0.8119999766349792},{"id":"https://openalex.org/keywords/partial-derivatives","display_name":"partial derivatives","score":0.6919999718666077},{"id":"https://openalex.org/keywords/sequential-design","display_name":"sequential design","score":0.48899999260902405},{"id":"https://openalex.org/keywords/passive-design","display_name":"passive design","score":0.6389999985694885},{"id":"https://openalex.org/keywords/local-polynomial-estimator","display_name":"local polynomial estimator","score":0.8899999856948853},{"id":"https://openalex.org/keywords/polynomial-time-algorithms","display_name":"polynomial-time algorithms","score":0.6629999876022339},{"id":"https://openalex.org/keywords/minimax-lower-bounds","display_name":"minimax lower bounds","score":0.6420000195503235},{"id":"https://openalex.org/keywords/upper-bounds","display_name":"upper bounds","score":0.48899999260902405},{"id":"https://openalex.org/keywords/smooth-functions","display_name":"smooth functions","score":0.3659999966621399}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7659000158309937},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7429999709129333},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.593500018119812},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5873000025749207},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5490999817848206},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5364000201225281},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5030999779701233},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4496999979019165},{"id":"https://openalex.org/C133939421","wikidata":"https://www.wikidata.org/wiki/Q6865379","display_name":"Minimax estimator","level":4,"score":0.37299999594688416},{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.3720000088214874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3425000011920929},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3391999900341034},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C117148685","wikidata":"https://www.wikidata.org/wiki/Q6865376","display_name":"Minimax approximation algorithm","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C98458673","wikidata":"https://www.wikidata.org/wiki/Q917657","display_name":"Step function","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C2780861221","wikidata":"https://www.wikidata.org/wiki/Q913849","display_name":"Minimax theorem","level":3,"score":0.26339998841285706},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.18678","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18678","pdf_url":"https://arxiv.org/pdf/2609.18678","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":"pmh:oai:HAL:hal-05750153v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05750153","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.18678","doi":"https://doi.org/10.48550/arxiv.2609.18678","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18678","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:2609.18678","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18678","pdf_url":"https://arxiv.org/pdf/2609.18678","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":[{"id":"https://openalex.org/G1527455529","display_name":null,"funder_award_id":"ANR\u201011\u2010LABEX\u20100047","funder_id":"https://openalex.org/F4320328775","funder_display_name":"Labex Ecodec"},{"id":"https://openalex.org/G3588620342","display_name":null,"funder_award_id":"11-LABEX-0047","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5442721034","display_name":"Machine Learning of Inverse Problems: Statistical Inference and Stochastic Optimization","funder_award_id":"ANR-25-CE40-3228","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6724645115","display_name":null,"funder_award_id":"LABEX-0047","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7629784203","display_name":null,"funder_award_id":"ANR-11-LABEX-0047","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320328775","display_name":"Labex Ecodec","ror":"https://ror.org/052q5t938"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213513824.pdf","grobid_xml":"https://content.openalex.org/works/W7213513824.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4399554463"],"related_works":["https://openalex.org/W7167800980","https://openalex.org/W3036190098","https://openalex.org/W4379539282","https://openalex.org/W4416123304","https://openalex.org/W7221756104","https://openalex.org/W7096498430","https://openalex.org/W2794722150","https://openalex.org/W4310515070","https://openalex.org/W3035736653","https://openalex.org/W3006717853"],"abstract_inverted_index":{"We":[0,23,76,133],"consider":[1],"the":[2,9,36,47,56,66,70,98,104,146,149,157,169],"problem":[3,57],"of":[4,8,14,35,58,62,81,145,148],"noisy":[5,59],"gradient-free":[6,60],"minimization":[7,61],"k-th":[10],"order":[11],"partial":[12],"derivative":[13],"a":[15,20,31,79,82,126,143],"$\u03b2$-H{\u00f6}lder":[16,63,127],"function":[17,128],"supported":[18],"on":[19,159],"d-dimensional":[21],"cube.":[22],"show":[24,77],"that":[25,78,101,123,141],"T":[26,37],"^{($\u03b2$+d+k)/(2$\u03b2$+d)}":[27],"log(T":[28],")^{(\u03b2-k)/(2\u03b2+d)}":[29],"is":[30,88,95,111,120,125],"non-asymptotic":[32],"minimax":[33,91],"rate":[34],"step":[38],"cumulative":[39],"regret":[40],"for":[41],"all":[42],"$\u03b2$":[43],"\\ge":[44],"0.":[45],"In":[46],"special":[48],"case":[49],"k":[50],"=":[51],"0,":[52],"our":[53],"results":[54],"cover":[55],"functions,":[64],"closing":[65],"existing":[67],"gap":[68],"between":[69],"known":[71,122],"upper":[72,93],"and":[73],"lower":[74,170],"bounds.":[75],"minimizer":[80,147],"suitably":[83],"chosen":[84],"local":[85,150],"polynomial":[86,139,151,165],"estimator":[87,158],"rate-optimal.":[89],"The":[90,153,163],"optimal":[92],"bound":[94],"achieved":[96],"under":[97],"passive":[99],"design,":[100],"is,":[102],"when":[103,118],"query":[105],"points":[106],"are":[107],"i.i.d.":[108],"Thus,":[109],"there":[110],"no":[112,130],"advantage":[113],"in":[114,138],"considering":[115],"sequential":[116],"designs":[117],"it":[119],"only":[121],"f":[124],"with":[129],"additional":[131],"property.":[132],"propose":[134],"an":[135],"algorithm":[136,167],"feasible":[137],"time":[140,166],"constructs":[142],"proxy":[144],"estimator.":[152],"procedure":[154],"requires":[155],"computing":[156],"auxiliary":[160],"random":[161],"points.":[162],"resulting":[164],"matches":[168],"bound.":[171]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-18T00:00:00"}
