{"id":"https://openalex.org/W7223147283","doi":"https://doi.org/10.48550/arxiv.2610.27681","title":"Adaptive Normalized Gradient Method for $(L_0,L_1)$-smooth Problems: Estimating Problem Parameters as a Region","display_name":"Adaptive Normalized Gradient Method for $(L_0,L_1)$-smooth Problems: Estimating Problem Parameters as a Region","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223147283","doi":"https://doi.org/10.48550/arxiv.2610.27681"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.27681","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27681","pdf_url":"https://arxiv.org/pdf/2610.27681","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/2610.27681","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112829129","display_name":"R. Okazaki","orcid":"https://orcid.org/0009-0006-2240-2336","observed_orcids":["https://orcid.org/0009-0006-2240-2336"]},"institutions":[{"id":"https://openalex.org/I200475212","display_name":"The Graduate University for Advanced Studies, SOKENDAI","ror":"https://ror.org/0516ah480","country_code":"JP","type":"education","lineage":["https://openalex.org/I200475212"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Okazaki, Rikiya","raw_affiliation_strings":["Graduate Institute for Advanced Studies , SOKENDAI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate Institute for Advanced Studies , SOKENDAI","institution_ids":["https://openalex.org/I200475212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070837037","display_name":"Shotaro Yagishita","orcid":"https://orcid.org/0000-0003-1946-5732","observed_orcids":["https://orcid.org/0000-0003-1946-5732"]},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yagishita, Shotaro","raw_affiliation_strings":["Graduate School of Informatics , Kyoto University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Informatics , Kyoto University","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023633849","display_name":"Hideitsu Hino","orcid":"https://orcid.org/0000-0002-6405-4361","observed_orcids":["https://orcid.org/0000-0002-6405-4361"]},"institutions":[{"id":"https://openalex.org/I200475212","display_name":"The Graduate University for Advanced Studies, SOKENDAI","ror":"https://ror.org/0516ah480","country_code":"JP","type":"education","lineage":["https://openalex.org/I200475212"]},{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hino, Hideitsu","raw_affiliation_strings":["Graduate Institute for Advanced Studies , SOKENDAI","The Institute of Statistical Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate Institute for Advanced Studies , SOKENDAI","institution_ids":["https://openalex.org/I200475212"]},{"raw_affiliation_string":"The Institute of Statistical Mathematics","institution_ids":["https://openalex.org/I4210134673"]}]}],"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9810000061988831,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9810000061988831,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.007899999618530273,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.003599999938160181,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/parameter-free-algorithms","display_name":"parameter-free algorithms","score":0.7860000133514404},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"gradient descent","score":0.5870000123977661},{"id":"https://openalex.org/keywords/iteration-complexity","display_name":"iteration complexity","score":0.7139999866485596},{"id":"https://openalex.org/keywords/nonconvex-optimization","display_name":"non-convex optimization","score":0.875},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"convex optimization","score":0.9010000228881836},{"id":"https://openalex.org/keywords/step-size-selection","display_name":"step size selection","score":0.8180000185966492},{"id":"https://openalex.org/keywords/logistic-regression","display_name":"logistic regression","score":0.9340000152587891}],"concepts":[{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.7192000150680542},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6381999850273132},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6177999973297119},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5572999715805054},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5256999731063843},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4650999903678894},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43939998745918274},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43070000410079956},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4090999960899353},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.40450000762939453},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39410001039505005},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.33959999680519104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3357999920845032},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.3276999890804291},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3158000111579895},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.28349998593330383},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.27681","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27681","pdf_url":"https://arxiv.org/pdf/2610.27681","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.2610.27681","doi":"https://doi.org/10.48550/arxiv.2610.27681","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.27681","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:2610.27681","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27681","pdf_url":"https://arxiv.org/pdf/2610.27681","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":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320338075","display_name":"Core Research for Evolutional Science and Technology","ror":"https://ror.org/00097mb19"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223147283.pdf","grobid_xml":"https://content.openalex.org/works/W7223147283.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W6977148848","https://openalex.org/W4403780428","https://openalex.org/W4320855041","https://openalex.org/W7171836607","https://openalex.org/W4416177826","https://openalex.org/W7163007304","https://openalex.org/W4388482188","https://openalex.org/W4405767363","https://openalex.org/W7160321266","https://openalex.org/W4414981742"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,39,45,108],"parameter-free":[3,110],"and":[4,52,135,146],"efficient":[5],"gradient":[6,30],"descent":[7],"algorithm":[8],"for":[9,50,74,107],"$(L_0,L_1)$-smooth":[10],"optimization.":[11],"This":[12],"notion":[13],"of":[14,41,47,97],"smoothness,":[15],"introduced":[16],"by":[17],"Zhang":[18],"et":[19],"al.":[20],"(2020),":[21],"allows":[22],"the":[23,29,61,67,81,95,102,112,117,123,128],"smoothness":[24],"bound":[25,71],"to":[26,33,43,56,105],"grow":[27],"with":[28],"norm.":[31],"Similar":[32],"cutting-plane":[34],"localization,":[35],"our":[36,64,98,141],"method":[37,65,142],"uses":[38,53],"sequence":[40],"observations":[42],"maintain":[44],"region":[46,55],"plausible":[48],"values":[49],"$(L_0,L_1)$":[51],"this":[54,100],"select":[57],"step":[58],"sizes.":[59],"In":[60],"convex":[62,129],"setting,":[63],"attains":[66],"standard":[68],"iteration":[69],"complexity":[70],"$\\tilde{\\mathcal{O}}\\left(\\left(L_0/\u03b5+":[72],"L_1^2\\right)\\|x^0-x^*\\|^2\\right)$":[73],"finding":[75],"an":[76,86],"$\u03b5$-optimal":[77],"solution,":[78],"while":[79,120],"in":[80,116,127],"nonconvex":[82,118,150],"setting":[83,119],"it":[84],"finds":[85],"$\u03b5$-stationary":[87],"point":[88],"within":[89],"$\\tilde{\\mathcal{O}}\\left(\\left(L_0/\u03b5^2":[90],"+":[91],"L_1/\u03b5\\right)(f(x^0)-f^*)\\right)$":[92],"iterations.":[93],"To":[94],"best":[96],"knowledge,":[99],"is":[101],"first":[103],"work":[104],"establish,":[106],"single":[109],"algorithm,":[111],"best-known":[113],"iteration-complexity":[114,125],"guarantee":[115,126],"also":[121],"providing":[122],"above":[124],"setting.":[130],"Experiments":[131],"on":[132,149],"logistic":[133],"regression":[134],"real":[136],"phase":[137],"retrieval":[138],"demonstrate":[139],"that":[140],"can":[143],"exploit":[144],"$(L_0,L_1)$-smoothness":[145],"perform":[147],"efficiently":[148],"problems.":[151]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-22T00:00:00"}