{"id":"https://openalex.org/W6966856580","doi":"https://doi.org/10.48550/arxiv.2505.17965","title":"Bias-Optimal Bounds for SGD: A Computer-Aided Lyapunov Analysis","display_name":"Bias-Optimal Bounds for SGD: A Computer-Aided Lyapunov Analysis","publication_year":2025,"publication_date":"2025-05-23","ids":{"openalex":"https://openalex.org/W6966856580","doi":"https://doi.org/10.48550/arxiv.2505.17965"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2505.17965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.17965","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2505.17965","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Cortild, Daniel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cortild, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Ketels, Lucas","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ketels, Lucas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Peypouquet, Juan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peypouquet, Juan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Garrigos, Guillaume","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Garrigos, Guillaume","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":true,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9079999923706055,"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":0.9079999923706055,"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":0.011500000022351742,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.009100000374019146,"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/convexity","display_name":"Convexity","score":0.715399980545044},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.7138000130653381},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.659600019454956},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5393000245094299},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5152000188827515},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5113000273704529},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.49410000443458557},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4925000071525574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7677000164985657},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.715399980545044},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.7138000130653381},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.659600019454956},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5825999975204468},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5393000245094299},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5152000188827515},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5113000273704529},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.49410000443458557},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4925000071525574},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.47279998660087585},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4465000033378601},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.44209998846054077},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.42260000109672546},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3944000005722046},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3910999894142151},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.37599998712539673},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35519999265670776},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2581000030040741}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2505.17965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.17965","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2505.17965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.17965","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,105],"non-asymptotic":[1],"analysis":[2],"of":[3,43,53,75,85,112,127,148],"Stochastic":[4],"Gradient":[5],"Descent":[6],"(SGD)":[7],"typically":[8],"yields":[9,119],"bounds":[10,59,106],"that":[11,60,66,97],"decompose":[12],"into":[13],"a":[14,18,113],"bias":[15,28,68],"term":[16,69],"and":[17,30,51,93],"variance":[19,103,151],"term.":[20],"In":[21],"this":[22,128],"work,":[23],"we":[24,56,130,138],"focus":[25],"on":[26],"the":[27,32,39,54,64,67,72,82,110,125,132,146,149],"component":[29],"study":[31],"extent":[33],"to":[34,141],"which":[35,137],"SGD":[36],"can":[37],"match":[38],"optimal":[40],"convergence":[41,121],"behavior":[42],"deterministic":[44],"gradient":[45,76],"descent.":[46,77],"Assuming":[47],"only":[48],"(strong)":[49],"convexity":[50],"smoothness":[52],"objective,":[55],"derive":[57],"new":[58],"are":[61,107],"bias-optimal,":[62],"in":[63],"sense":[65],"coincides":[70],"with":[71],"worst-case":[73],"rate":[74],"Our":[78],"results":[79],"hold":[80],"for":[81,145],"full":[83],"range":[84],"constant":[86],"step-sizes":[87],"$\u03b3L":[88],"\\in":[89],"(0,2)$,":[90],"including":[91],"critical":[92],"large":[94],"step-size":[95],"regimes":[96],"were":[98],"previously":[99],"unexplored":[100],"without":[101],"additional":[102],"assumptions.":[104],"obtained":[108],"through":[109],"construction":[111],"simple":[114],"Lyapunov":[115],"energy":[116],"whose":[117],"monotonicity":[118],"sharp":[120],"guarantees.":[122],"To":[123],"design":[124],"parameters":[126],"energy,":[129],"employ":[131],"Performance":[133],"Estimation":[134],"Problem":[135],"framework,":[136],"also":[139],"use":[140],"provide":[142],"numerical":[143],"evidence":[144],"optimality":[147],"associated":[150],"terms.":[152]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}