{"id":"https://openalex.org/W4281799119","doi":"https://doi.org/10.1145/3489048.3522659","title":"Stationary Behavior of Constant Stepsize SGD Type Algorithms","display_name":"Stationary Behavior of Constant Stepsize SGD Type Algorithms","publication_year":2022,"publication_date":"2022-06-02","ids":{"openalex":"https://openalex.org/W4281799119","doi":"https://doi.org/10.1145/3489048.3522659"},"language":"en","primary_location":{"id":"doi:10.1145/3489048.3522659","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3489048.3522659","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Abstract Proceedings of the 2022 ACM SIGMETRICS/IFIP PERFORMANCE Joint International Conference on Measurement and Modeling of Computer Systems","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058269077","display_name":"Zaiwei Chen","orcid":"https://orcid.org/0000-0001-9915-5595"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zaiwei Chen","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, GA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067794264","display_name":"Shancong Mou","orcid":"https://orcid.org/0000-0003-2481-3308"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shancong Mou","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, GA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021806638","display_name":"Siva Theja Maguluri","orcid":"https://orcid.org/0000-0002-5797-1639"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Siva Theja Maguluri","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, GA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05551536,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"109","last_page":"110"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9973999857902527,"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":0.9973999857902527,"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/T10320","display_name":"Neural Networks and Applications","score":0.9879000186920166,"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/T11716","display_name":"Random Matrices and Applications","score":0.9722999930381775,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.706204891204834},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5468277335166931},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.49096038937568665},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4811466932296753},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.44506123661994934},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4209108352661133},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.417527973651886},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34051647782325745},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30184757709503174},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1594197154045105}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.706204891204834},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5468277335166931},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.49096038937568665},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4811466932296753},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.44506123661994934},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4209108352661133},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.417527973651886},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34051647782325745},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30184757709503174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1594197154045105},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3489048.3522659","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3489048.3522659","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Abstract Proceedings of the 2022 ACM SIGMETRICS/IFIP PERFORMANCE Joint International Conference on Measurement and Modeling of Computer Systems","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2793786119","https://openalex.org/W1507702947","https://openalex.org/W3150057971"],"abstract_inverted_index":{"Stochastic":[0],"approximation":[1],"(SA)":[2],"and":[3,91,103,201,228],"stochastic":[4,239],"gradient":[5],"descent":[6],"(SGD)":[7],"algorithms":[8,33,178],"are":[9,20],"work-horses":[10],"for":[11,237],"modern":[12],"machine":[13],"learning":[14],"algorithms.":[15],"Their":[16],"constant":[17,30,73,123],"stepsize":[18,31,74],"variants":[19],"preferred":[21],"in":[22,48,68,148],"practice":[23],"due":[24],"to":[25,37,76,222,232],"fast":[26],"convergence":[27],"behavior.":[28],"However,":[29],"SA":[32,97,106,177],"do":[34],"not":[35,198,207],"converge":[36],"the":[38,59,63,69,72,81,113,122,128,157,168,194,203,212,224,233],"optimal":[39],"solution,":[40],"but":[41],"instead":[42],"have":[43],"a":[44,89,100,109,134,141,161,219,230],"stationary":[45,66,131],"distribution,":[46,67],"which":[47],"general":[49],"cannot":[50],"be":[51,146,199,208],"analytically":[52],"characterized.":[53],"In":[54],"this":[55,152],"work,":[56],"we":[57,79,125,154,215],"study":[58],"asymptotic":[60],"behavior":[61],"of":[62,136,171],"appropriately":[64],"scaled":[65,116,130],"limit":[70,189],"when":[71],"goes":[75],"zero.":[77],"Specifically,":[78],"consider":[80],"following":[82],"three":[83],"settings:":[84],"(1)":[85,193],"SGD":[86],"algorithm":[87,98,107],"with":[88,218],"smooth":[90],"strongly":[92],"convex":[93],"objective,":[94],"(2)":[95,202],"linear":[96],"involving":[99,108],"Hurwitz":[101],"matrix,":[102],"(3)":[104],"nonlinear":[105],"contractive":[110],"operator.":[111],"When":[112],"iterate":[114],"is":[115,121,133,167],"by":[117],"1/\u221a\u03b1,":[118,200],"where":[119],"\u03b1":[120],"stepsize,":[124],"show":[126],"that":[127,186],"limiting":[129,158,204],"distribution":[132,159,163,205],"solution":[135,170],"an":[137,172],"implicit":[138],"equation.":[139,175],"Under":[140],"uniqueness":[142],"assumption":[143],"(which":[144],"can":[145],"removed":[147],"certain":[149],"settings)":[150],"on":[151,211],"equation,":[153],"further":[155],"characterize":[156],"as":[160],"Gaussian":[162],"whose":[164],"covariance":[165],"matrix":[166],"unique":[169],"appropriate":[173],"Lyapunov":[174],"For":[176],"beyond":[179],"these":[180],"cases,":[181],"our":[182],"numerical":[183,213],"experiments":[184],"suggest":[185],"unlike":[187],"central":[188],"theorem":[190],"type":[191],"results:":[192],"scaling":[195,226],"factor":[196],"need":[197,206],"Gaussian.":[209],"Based":[210],"study,":[214],"come":[216],"up":[217],"heuristic":[220],"formula":[221],"determine":[223],"right":[225],"factor,":[227],"make":[229],"connection":[231],"Euler-Maruyama":[234],"discretization":[235],"scheme":[236],"approximating":[238],"differential":[240],"equations.":[241]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}