{"id":"https://openalex.org/W7161557512","doi":"https://doi.org/10.48550/arxiv.2605.15314","title":"Beyond Bounded Variance: Variance-Reduced Normalized Methods for Nonconvex Optimization under Blum-Gladyshev Noise","display_name":"Beyond Bounded Variance: Variance-Reduced Normalized Methods for Nonconvex Optimization under Blum-Gladyshev Noise","publication_year":2026,"publication_date":"2026-05-14","ids":{"openalex":"https://openalex.org/W7161557512","doi":"https://doi.org/10.48550/arxiv.2605.15314"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.15314","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15314","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":"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.15314","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064442263","display_name":"Antesh Upadhyay","orcid":"https://orcid.org/0000-0001-7185-3690"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Upadhyay, Antesh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072651639","display_name":"Arda Fazla","orcid":"https://orcid.org/0000-0001-6763-7266"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fazla, Arda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136406409","display_name":"Abolfazl Hashemi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hashemi, Abolfazl","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":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9674999713897705,"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":0.9674999713897705,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.007600000128149986,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.004100000020116568,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/smoothness","display_name":"Smoothness","score":0.8519999980926514},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6262999773025513},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5357000231742859},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.4814999997615814},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.48030000925064087},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4496999979019165},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.4399999976158142},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.4146000146865845},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.39410001039505005}],"concepts":[{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.8519999980926514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7231000065803528},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6262999773025513},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5357000231742859},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4887999892234802},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.4814999997615814},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.48030000925064087},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4496999979019165},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.4399999976158142},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4235000014305115},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.39410001039505005},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.3910999894142151},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3808000087738037},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.38019999861717224},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.3684999942779541},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.32600000500679016},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3125},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.2971000075340271},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29100000858306885},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2822999954223633},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.2770000100135803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.15314","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15314","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.15314","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15314","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":"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"},"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":{"We":[0,24,49,97],"study":[1,99],"nonconvex":[2],"stochastic":[3,13,53,61,190],"optimization":[4,191],"under":[5,28,66,192],"the":[6,12,19,22,33,46,111,114,120,128,148,152,159,173,181],"Blum-Gladyshev":[7],"($\\mathsf{BG}$-0)":[8],"noise":[9,68,153,194],"model,":[10],"where":[11],"gradient":[14,47,54,62],"variance":[15,168],"grows":[16],"quadratically":[17],"with":[18,45,56,69,134],"distance":[20],"from":[21],"initialization.":[23],"consider":[25],"this":[26,95],"problem":[27],"both":[29,76,205],"standard":[30,78,160,206],"smoothness":[31,79,88,107,133,209],"and":[32,80,108,143,170,207],"symmetric":[34],"generalized-smoothness":[35],"framework,":[36],"which":[37],"captures":[38],"objectives":[39],"whose":[40],"local":[41],"curvature":[42],"can":[43],"scale":[44],"norm.":[48],"prove":[50],"that":[51,86],"normalized":[52,92,102,186],"descent":[55],"momentum,":[57,165],"using":[58],"only":[59],"one":[60],"per":[63],"iteration,":[64],"converges":[65],"$\\mathsf{BG}$-0":[67,193],"oracle":[70],"complexity":[71,139],"$O(\\varepsilon^{-6})$.":[72],"This":[73],"rate":[74],"holds":[75],"for":[77,81,91,141,145,164,167,185],"$\u03b1$-symmetric":[82,125],"generalized":[83,87,126,208],"smoothness,":[84,127],"showing":[85],"is":[89],"rate-neutral":[90],"momentum":[93],"in":[94,151,172,188],"setting.":[96],"then":[98],"a":[100],"variance-reduced":[101],"STORM":[103,129],"method.":[104],"Under":[105,123],"mean-square":[106],"sharp":[109],"initialization,":[110],"method":[112],"achieves":[113],"minimax":[115],"optimal":[116],"$O(\\varepsilon^{-4})$":[117,163],"complexity,":[118],"matching":[119],"lower":[121],"bound.":[122],"expected":[124],"recursion":[130],"couples":[131],"gradient-dependent":[132],"distance-dependent":[135],"noise,":[136],"leading":[137],"to":[138],"$O(\\varepsilon^{-(4+\u03b1)})$":[140],"$\u03b1\\in(0,1)$":[142],"$O(\\varepsilon^{-5})$":[144],"$\u03b1=1$.":[146],"When":[147],"distance-growth":[149],"parameter":[150],"model":[154],"vanishes,":[155],"our":[156,177],"guarantees":[157,184],"recover":[158],"bounded-variance":[161],"rates:":[162],"$O(\\varepsilon^{-3})$":[166],"reduction,":[169],"$O(\\varepsilon^{-2})$":[171],"deterministic":[174],"case.":[175],"To":[176],"knowledge,":[178],"these":[179],"are":[180],"first":[182],"convergence":[183],"methods":[187],"non-convex":[189],"without":[195],"bounded":[196],"domains,":[197],"increasing":[198],"batch":[199],"sizes,":[200],"or":[201],"explicit":[202],"anchoring,":[203],"covering":[204],"regimes.":[210]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-19T00:00:00"}