{"id":"https://openalex.org/W7125851080","doi":"https://doi.org/10.1137/24m1704154","title":"Large Deviation Upper Bounds and Improved MSE Rates of Nonlinear SGD: Heavy-Tailed Noise and Power of Symmetry","display_name":"Large Deviation Upper Bounds and Improved MSE Rates of Nonlinear SGD: Heavy-Tailed Noise and Power of Symmetry","publication_year":2026,"publication_date":"2026-01-27","ids":{"openalex":"https://openalex.org/W7125851080","doi":"https://doi.org/10.1137/24m1704154"},"language":"en","primary_location":{"id":"doi:10.1137/24m1704154","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1704154","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://infoscience.epfl.ch/handle/20.500.14299/258644","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124040876","display_name":"Aleksandar Armacki","orcid":null},"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":"Aleksandar Armacki","raw_affiliation_strings":["School of Engineering, EPFL, 1015 Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering, EPFL, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123948629","display_name":"Shuhua Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuhua Yu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890 USA"],"raw_orcid":"https://orcid.org/0000-0002-6054-673X","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890 USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124031908","display_name":"Dragana Bajovi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Dragana Bajovi\u0107","raw_affiliation_strings":["Faculty of Technical Sciences, Department of Power, Electronic, and Communication Engineering, University of Novi Sad, 21000 Novi Sad, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Technical Sciences, Department of Power, Electronic, and Communication Engineering, University of Novi Sad, 21000 Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124035300","display_name":"Du\u0161an Jakoveti\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Du\u0161an Jakoveti\u0107","raw_affiliation_strings":["Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077268766","display_name":"Soummya Kar","orcid":"https://orcid.org/0000-0002-8060-5581"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Soummya Kar","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890 USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5102,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.84191324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"36","issue":"1","first_page":"32","last_page":"59"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10232","display_name":"Optical Network Technologies","score":0.2484000027179718,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10232","display_name":"Optical Network Technologies","score":0.2484000027179718,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10988","display_name":"Advanced Fiber Laser Technologies","score":0.1396999955177307,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.08590000122785568,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5870000123977661},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5327000021934509},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5230000019073486},{"id":"https://openalex.org/keywords/large-deviations-theory","display_name":"Large deviations theory","score":0.4851999878883362},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.47380000352859497}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8251000046730042},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5870000123977661},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5327000021934509},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5230000019073486},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.4851999878883362},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.47380000352859497},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45190000534057617},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4413999915122986},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.30329999327659607},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.28949999809265137}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/24m1704154","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1704154","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:20.500.14299/258644","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/258644","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"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":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:20.500.14299/258644","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/258644","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"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":"research article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G740059604","display_name":null,"funder_award_id":"01-3394/1","funder_id":"https://openalex.org/F8499512009","funder_display_name":"University of Novi Sad"}],"funders":[{"id":"https://openalex.org/F8499512009","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1502405545","https://openalex.org/W1971942712","https://openalex.org/W1972633005","https://openalex.org/W1992208280","https://openalex.org/W1994616650","https://openalex.org/W2024484010","https://openalex.org/W2045744861","https://openalex.org/W2051359738","https://openalex.org/W2079363091","https://openalex.org/W2086161653","https://openalex.org/W2114346036","https://openalex.org/W2127484045","https://openalex.org/W2796146910","https://openalex.org/W2901838001","https://openalex.org/W2963433607","https://openalex.org/W2963470657","https://openalex.org/W2993258424","https://openalex.org/W2994760360","https://openalex.org/W3025638325","https://openalex.org/W4220913814","https://openalex.org/W4250954493","https://openalex.org/W4280634204","https://openalex.org/W4377013551","https://openalex.org/W4378764988","https://openalex.org/W4387665618","https://openalex.org/W4399437517"],"related_works":[],"abstract_inverted_index":{"Abstract.":[0],"We":[1,84,149],"study":[2],"large":[3,124],"deviation":[4,125],"upper":[5,126],"bounds":[6],"and":[7,26,81,112,166,173,193],"mean":[8],"squared":[9],"error":[10],"(MSE)":[11],"guarantees":[12,88],"of":[13,17,30,42,66,93,98,110,132,162,177,223,233,237],"a":[14,43,53,63,90,108,123,144],"general":[15],"framework":[16,48],"nonlinear":[18],"stochastic":[19],"gradient":[20],"methods":[21],"in":[22,27,52,95,107,220],"the":[23,28,39,50,96,129,151,160,174,181,194,209,217,221,234],"online":[24],"setting":[25],"presence":[29,97,222],"heavy-tailed":[31,99,224],"noise.":[32,225],"Unlike":[33],"existing":[34],"works":[35],"that":[36,202],"rely":[37],"on":[38,139,159,216],"closed":[40],"form":[41],"nonlinearity":[44,51],"(typically":[45],"clipping),":[46],"our":[47],"treats":[49],"black-box":[54],"manner,":[55],"allowing":[56],"us":[57],"to":[58,208,249],"provide":[59,85,122,198],"unified":[60],"results":[61,219],"for":[62,89,118,128,170,189],"broad":[64,91],"class":[65],"bounded":[67],"nonlinearities,":[68],"including":[69],"many":[70],"popular":[71],"ones,":[72],"like":[73],"sign,":[74],"quantization,":[75],"normalization,":[76],"as":[77,79],"well":[78],"componentwise":[80],"joint":[82],"clipping.":[83],"several":[86],"strong":[87],"range":[92],"step-sizes":[94],"noise":[100],"with":[101],"symmetric":[102],"probability":[103],"density":[104],"function,":[105,154],"positive":[106],"neighborhood":[109],"zero":[111],"potentially":[113],"unbounded":[114],"moments.":[115],"In":[116],"particular,":[117],"nonconvex":[119,171],"costs,":[120],"we":[121,179,197,227],"bound":[127],"minimum":[130,175,235],"norm-squared":[131,176,236],"gradients,":[133,178,238],"showing":[134,155],"an":[135,140,156,199,240],"asymptotic":[136],"tail":[137],"decay":[138],"exponential":[141],"scale,":[142],"at":[143],"rate":[145,153,184,201,211,242],"[Formula:":[146,185,212,250],"see":[147,186,213,251],"text].":[148,187,252],"establish":[150,228],"accompanying":[152],"explicit":[157,241],"dependence":[158],"choice":[161],"step-size,":[163],"nonlinearity,":[164],"noise,":[165],"problem":[167],"parameters.":[168],"Next,":[169],"costs":[172,192],"derive":[180],"optimal":[182,210],"MSE":[183,200],"Moreover,":[188],"strongly":[190],"convex":[191],"last":[195],"iterate,":[196],"can":[203,244],"be":[204,245],"made":[205,246],"arbitrarily":[206,247],"close":[207,248],"text],":[214],"improving":[215],"state-of-the-art":[218],"Finally,":[226],"almost":[229],"sure":[230],"(a.s.)":[231],"convergence":[232],"providing":[239],"which":[243]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2026-01-28T00:00:00"}