{"id":"https://openalex.org/W7224843045","doi":"https://doi.org/10.48550/arxiv.2610.39716","title":"Adaptive Federated Optimization Across Smooth and Nonsmooth Regimes","display_name":"Adaptive Federated Optimization Across Smooth and Nonsmooth Regimes","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224843045","doi":"https://doi.org/10.48550/arxiv.2610.39716"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.39716","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39716","pdf_url":"https://arxiv.org/pdf/2610.39716","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.39716","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160226336","display_name":"Zimeng Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I90267481","display_name":"Ume\u00e5 University","ror":"https://ror.org/05kb8h459","country_code":"SE","type":"education","lineage":["https://openalex.org/I90267481"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Wang, Zimeng","raw_affiliation_strings":["Department of Mathematics and Mathematical Statistics , Ume\u00e5 University , Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mathematical Statistics , Ume\u00e5 University , Sweden","institution_ids":["https://openalex.org/I90267481"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093826620","display_name":"Ali Dadras","orcid":"https://orcid.org/0000-0003-1134-2615","observed_orcids":["https://orcid.org/0000-0003-1134-2615"]},"institutions":[{"id":"https://openalex.org/I90267481","display_name":"Ume\u00e5 University","ror":"https://ror.org/05kb8h459","country_code":"SE","type":"education","lineage":["https://openalex.org/I90267481"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Dadras, Ali","raw_affiliation_strings":["Department of Mathematics and Mathematical Statistics , Ume\u00e5 University , Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mathematical Statistics , Ume\u00e5 University , Sweden","institution_ids":["https://openalex.org/I90267481"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043683448","display_name":"Alp Yurtsever","orcid":"https://orcid.org/0000-0001-7320-1506","observed_orcids":["https://orcid.org/0000-0001-7320-1506"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yurtsever, Alp","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8363999724388123,"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":0.8363999724388123,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.15629999339580536,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.0019000000320374966,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/federated-optimization","display_name":"federated optimization","score":0.9700000286102295},{"id":"https://openalex.org/keywords/adaptive-learning-rate","display_name":"adaptive learning rate","score":0.5879999995231628},{"id":"https://openalex.org/keywords/adagrad","display_name":"AdaGrad","score":0.7889999747276306},{"id":"https://openalex.org/keywords/nonsmooth-optimization","display_name":"nonsmooth optimization","score":0.7440000176429749},{"id":"https://openalex.org/keywords/nonconvex-optimization","display_name":"non-convex optimization","score":0.8650000095367432},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"convex optimization","score":0.7149999737739563},{"id":"https://openalex.org/keywords/stochastic-gradient-noise","display_name":"stochastic gradient noise","score":0.8330000042915344},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.8270000219345093}],"concepts":[{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.8007000088691711},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7199000120162964},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6858000159263611},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6633999943733215},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5636000037193298},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5314000248908997},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5149000287055969},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5121999979019165},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4925999939441681},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.48829999566078186},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4404999911785126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4036000072956085},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3765000104904175},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.3508000075817108},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2904999852180481},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.39716","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39716","pdf_url":"https://arxiv.org/pdf/2610.39716","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.2610.39716","doi":"https://doi.org/10.48550/arxiv.2610.39716","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.39716","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.39716","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39716","pdf_url":"https://arxiv.org/pdf/2610.39716","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/G93431365","display_name":"Advances in Federated Learning: Addressing Emerging Challenges and Expanding Frontiers through Optimization Theory","funder_award_id":"2023-05476","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224843045.pdf","grobid_xml":"https://content.openalex.org/works/W7224843045.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3008187686","https://openalex.org/W4388328981","https://openalex.org/W4405075336","https://openalex.org/W7160326924","https://openalex.org/W4385576052","https://openalex.org/W4389111296","https://openalex.org/W4285787401","https://openalex.org/W4315488555","https://openalex.org/W4407209162","https://openalex.org/W4320561688"],"abstract_inverted_index":{"AdaGrad-style":[0],"methods":[1],"can":[2],"simultaneously":[3],"adapt":[4],"to":[5,19,34,87,99],"both":[6,70],"the":[7,31,60,100,112],"order":[8,33],"and":[9,26,73,77,107],"constants":[10],"of":[11,57],"smoothness":[12,32],"in":[13,37],"centralized":[14],"optimization.":[15],"However,":[16],"existing":[17],"extensions":[18],"federated":[20,46],"optimization":[21],"with":[22,43,103],"heterogeneous":[23],"client":[24],"objectives":[25,85],"multiple":[27],"local":[28],"steps":[29],"require":[30],"be":[35],"specified":[36],"advance.":[38],"We":[39],"address":[40],"this":[41],"limitation":[42],"AdaFed,":[44],"a":[45,54,91],"method":[47],"that":[48],"adapts":[49],"across":[50,111],"several":[51],"regimes":[52],"under":[53],"single":[55],"choice":[56],"parameters.":[58],"In":[59],"deterministic":[61],"setting,":[62],"AdaFed":[63],"achieves":[64],"an":[65,78],"$O(1/T)$":[66],"convergence":[67],"rate":[68,80],"for":[69,81],"smooth":[71,74],"nonconvex":[72],"convex":[75,84],"objectives,":[76],"$O(1/\\sqrt{T})$":[79],"Lipschitz":[82],"nonsmooth":[83],"up":[86],"logarithmic":[88,105],"factors.":[89],"Under":[90],"light-tailed":[92],"stochastic-gradient":[93],"noise":[94],"assumption,":[95],"these":[96],"guarantees":[97],"extend":[98],"stochastic":[101],"setting":[102],"additional":[104],"factors":[106],"noise-dependent":[108],"terms.":[109],"Experiments":[110],"three":[113],"problem":[114],"classes":[115],"further":[116],"support":[117],"our":[118],"theoretical":[119],"findings.":[120]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-31T00:00:00"}