{"id":"https://openalex.org/W7220978541","doi":"https://doi.org/10.48550/arxiv.2610.10527","title":"Decentralized SGD under Heavy-Tailed Noise: Optimal Convergence Rates and the Role of Gradient Clipping","display_name":"Decentralized SGD under Heavy-Tailed Noise: Optimal Convergence Rates and the Role of Gradient Clipping","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220978541","doi":"https://doi.org/10.48550/arxiv.2610.10527"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10527","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10527","pdf_url":"https://arxiv.org/pdf/2610.10527","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/2610.10527","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043355874","display_name":"Aleksandar Armacki","orcid":"https://orcid.org/0000-0001-7916-585X","observed_orcids":["https://orcid.org/0000-0001-7916-585X"]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Armacki, Aleksandar","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , Lausanne , Switzerland,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , Lausanne , Switzerland,","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157933871","display_name":"Haoyuan Cai","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Cai, Haoyuan","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , Lausanne , Switzerland,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , Lausanne , Switzerland,","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091103447","display_name":"Ali H. Sayed","orcid":"https://orcid.org/0000-0002-5125-5519","observed_orcids":["https://orcid.org/0000-0002-5125-5519"]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Sayed, Ali H.","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , Lausanne , Switzerland,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , Lausanne , Switzerland,","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I5124864"],"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":0.8798999786376953,"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":0.8798999786376953,"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":0.11349999904632568,"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"}},{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.0008999999845400453,"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/heavy-tailed-noise","display_name":"heavy-tailed noise","score":0.9350000023841858},{"id":"https://openalex.org/keywords/gradient-clipping","display_name":"gradient clipping","score":0.9940000176429749},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.6159999966621399},{"id":"https://openalex.org/keywords/nonconvex-optimization","display_name":"non-convex optimization","score":0.8679999709129333},{"id":"https://openalex.org/keywords/linear-speedup","display_name":"linear speedup","score":0.6579999923706055},{"id":"https://openalex.org/keywords/gradient-normalization","display_name":"gradient normalization","score":0.6460000276565552},{"id":"https://openalex.org/keywords/distributed-optimization","display_name":"distributed optimization","score":0.4390000104904175}],"concepts":[{"id":"https://openalex.org/C2776848632","wikidata":"https://www.wikidata.org/wiki/Q853463","display_name":"Clipping (morphology)","level":2,"score":0.7508000135421753},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.7379000186920166},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5361999869346619},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5249000191688538},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5070000290870667},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48159998655319214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48089998960494995},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40959998965263367},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.398499995470047},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.325300008058548},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32190001010894775},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.3059999942779541},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.29490000009536743},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.27630001306533813},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.26100000739097595}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10527","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10527","pdf_url":"https://arxiv.org/pdf/2610.10527","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.2610.10527","doi":"https://doi.org/10.48550/arxiv.2610.10527","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10527","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:2610.10527","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10527","pdf_url":"https://arxiv.org/pdf/2610.10527","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220978541.pdf","grobid_xml":"https://content.openalex.org/works/W7220978541.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1992208280","https://openalex.org/W2029080014","https://openalex.org/W2068254488","https://openalex.org/W2108306501","https://openalex.org/W2118776392","https://openalex.org/W2266148951","https://openalex.org/W2789912105","https://openalex.org/W2953881522","https://openalex.org/W2955291764","https://openalex.org/W2963470657","https://openalex.org/W2963649943","https://openalex.org/W2991772480","https://openalex.org/W3011252985","https://openalex.org/W4238850922","https://openalex.org/W4377013551","https://openalex.org/W4378764988","https://openalex.org/W4384831952","https://openalex.org/W4388006766","https://openalex.org/W4403308611","https://openalex.org/W4403425338","https://openalex.org/W4406047646","https://openalex.org/W4406523083","https://openalex.org/W4413408172","https://openalex.org/W7124589875"],"related_works":["https://openalex.org/W4415249256","https://openalex.org/W4388006766","https://openalex.org/W4414982464","https://openalex.org/W4403425338","https://openalex.org/W4404260997","https://openalex.org/W4403580163","https://openalex.org/W7124589875","https://openalex.org/W7167916285","https://openalex.org/W7124738905","https://openalex.org/W4320721098"],"abstract_inverted_index":{"Heavy-tailed":[0],"noise":[1],"has":[2,146],"been":[3,148],"widely":[4],"observed":[5],"in":[6,26,33,129,137,189],"modern":[7],"machine":[8],"learning,":[9],"motivating":[10],"the":[11,79,138,164,169],"use":[12],"of":[13,140,163,171],"methods":[14,22,152],"like":[15],"gradient":[16],"clipping":[17,57,64,186,199],"and":[18,46,58,68,128,187,208],"normalization.":[19],"While":[20],"these":[21],"are":[23],"well":[24],"understood":[25],"centralized":[27],"settings,":[28],"much":[29],"less":[30],"is":[31,159],"known":[32],"decentralized":[34,51,84,101,151,190],"ones,":[35],"where":[36],"applying":[37],"a":[38,82,87,134,160],"nonlinearity":[39,88],"to":[40,75,143,176,197,205],"local":[41,71],"gradients":[42],"affects":[43],"both":[44,56,124],"optimization":[45,53],"consensus.":[47],"Recent":[48],"works":[49],"on":[50],"non-convex":[52,106],"have":[54],"studied":[55],"normalization":[59,69,188],"under":[60,93,108],"heavy-tailed":[61,94],"noise,":[62,112],"with":[63,99,125,153],"yielding":[65],"suboptimal":[66],"rates":[67,92,123],"needing":[70],"momentum":[72],"or":[73],"mini-batches":[74],"converge.":[76],"This":[77],"raises":[78],"question:":[80],"can":[81,195],"baseline":[83],"method":[85],"using":[86],"achieve":[89],"optimal":[90],"convergence":[91],"noise?":[95],"We":[96],"answer":[97],"affirmatively":[98],"clipped":[100,119],"SGD":[102],"($\\mathtt{DSGD}$).":[103],"For":[104],"smooth":[105],"costs":[107],"bounded":[109],"$p$-th":[110],"moment":[111],"$p":[113],"\\in":[114],"(1,2]$,":[115],"we":[116,132],"show":[117],"that":[118,167],"$\\mathtt{DSGD}$":[120,194,204],"achieves":[121],"order-optimal":[122],"high":[126],"probability":[127],"expectation.":[130],"Moreover,":[131],"establish":[133],"linear":[135],"speed-up":[136],"number":[139],"agents,":[141],"which,":[142],"our":[144,213],"knowledge,":[145],"not":[147],"shown":[149],"for":[150],"clipping.":[154],"The":[155],"key":[156],"technical":[157],"ingredient":[158],"sharp":[161],"analysis":[162],"consensus":[165],"gap":[166],"exploits":[168],"structure":[170],"clipping,":[172],"relegating":[173],"network":[174],"effects":[175],"higher-order":[177],"terms.":[178],"Our":[179],"results":[180],"highlight":[181],"an":[182],"important":[183],"distinction":[184],"between":[185],"settings:":[191],"while":[192],"normalized":[193],"fail":[196],"converge,":[198],"retains":[200],"magnitude":[201],"information,":[202],"enabling":[203],"be":[206],"convergent":[207],"order-optimal.":[209],"Numerical":[210],"experiments":[211],"validate":[212],"theory.":[214]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}