{"id":"https://openalex.org/W3047780503","doi":"https://doi.org/10.1109/tsp.2021.3062553","title":"An Improved Convergence Analysis for Decentralized Online Stochastic Non-Convex Optimization","display_name":"An Improved Convergence Analysis for Decentralized Online Stochastic Non-Convex Optimization","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3047780503","doi":"https://doi.org/10.1109/tsp.2021.3062553","mag":"3047780503"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2021.3062553","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3062553","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2008.04195","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033024261","display_name":"Ran Xin","orcid":"https://orcid.org/0000-0002-1697-9116"},"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":"Ran Xin","raw_affiliation_strings":["ECE Department, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1697-9116","affiliations":[{"raw_affiliation_string":"ECE Department, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025641667","display_name":"Usman A. Khan","orcid":"https://orcid.org/0000-0002-0853-6518"},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Usman A. Khan","raw_affiliation_strings":["Electrical and Computer Engineering Department, Tufts University, Medford, MA, USA"],"raw_orcid":"https://orcid.org/0000-0002-0853-6518","affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, Tufts University, Medford, MA, USA","institution_ids":["https://openalex.org/I121934306"]}]},{"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":["ECE Department, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0000-0002-8060-5581","affiliations":[{"raw_affiliation_string":"ECE Department, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.1939,"has_fulltext":false,"cited_by_count":99,"citation_normalized_percentile":{"value":0.97945199,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"69","issue":null,"first_page":"1842","last_page":"1858"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9980999827384949,"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/sublinear-function","display_name":"Sublinear function","score":0.7665845155715942},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6963710784912109},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.6005631685256958},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.589390754699707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5771425366401672},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5704682469367981},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5684611797332764},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4958737790584564},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47390997409820557},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.4315488636493683},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4235735237598419},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3661520481109619},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3369855284690857},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.16351467370986938},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.14214381575584412}],"concepts":[{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.7665845155715942},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6963710784912109},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.6005631685256958},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.589390754699707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5771425366401672},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5704682469367981},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5684611797332764},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4958737790584564},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47390997409820557},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.4315488636493683},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4235735237598419},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3661520481109619},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3369855284690857},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.16351467370986938},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.14214381575584412},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2021.3062553","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3062553","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2008.04195","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.04195","pdf_url":"https://arxiv.org/pdf/2008.04195","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2008.04195","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.04195","pdf_url":"https://arxiv.org/pdf/2008.04195","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W1498711961","https://openalex.org/W1568288633","https://openalex.org/W1571416372","https://openalex.org/W1577337550","https://openalex.org/W1984884414","https://openalex.org/W1994860969","https://openalex.org/W2029080014","https://openalex.org/W2066332749","https://openalex.org/W2068254488","https://openalex.org/W2153368486","https://openalex.org/W2266148951","https://openalex.org/W2291434103","https://openalex.org/W2400034325","https://openalex.org/W2609549560","https://openalex.org/W2610857016","https://openalex.org/W2617960902","https://openalex.org/W2763533254","https://openalex.org/W2789243870","https://openalex.org/W2792298817","https://openalex.org/W2792751837","https://openalex.org/W2886474253","https://openalex.org/W2892002891","https://openalex.org/W2899734758","https://openalex.org/W2902410171","https://openalex.org/W2954270931","https://openalex.org/W2962771678","https://openalex.org/W2962989062","https://openalex.org/W2963228337","https://openalex.org/W2963248893","https://openalex.org/W2963433607","https://openalex.org/W2963649943","https://openalex.org/W2964165783","https://openalex.org/W2971384159","https://openalex.org/W2977517840","https://openalex.org/W2981831462","https://openalex.org/W2991772480","https://openalex.org/W2993488539","https://openalex.org/W3009274618","https://openalex.org/W3010627535","https://openalex.org/W3011252985","https://openalex.org/W3022621540","https://openalex.org/W3023944502","https://openalex.org/W3026733282","https://openalex.org/W3042491641","https://openalex.org/W3048505912","https://openalex.org/W3097497066","https://openalex.org/W3099715789","https://openalex.org/W3100513551","https://openalex.org/W3118568858","https://openalex.org/W3134022240","https://openalex.org/W4229706427","https://openalex.org/W4288288021","https://openalex.org/W4299802343","https://openalex.org/W6748632073","https://openalex.org/W6754297394","https://openalex.org/W6756976665","https://openalex.org/W6767487546","https://openalex.org/W6774136274","https://openalex.org/W6774700444","https://openalex.org/W6777541487"],"related_works":["https://openalex.org/W2149119057","https://openalex.org/W4286899070","https://openalex.org/W4323366756","https://openalex.org/W3207830353","https://openalex.org/W4285259204","https://openalex.org/W3109198354","https://openalex.org/W937081240","https://openalex.org/W2962798807","https://openalex.org/W4281666478","https://openalex.org/W4224283687"],"abstract_inverted_index":{"In":[0,45,74],"this":[1],"paper,":[2],"we":[3,26,52,106,127],"study":[4],"decentralized":[5,22],"online":[6],"stochastic":[7,23,124],"non-convex":[8,43,50,98],"optimization":[9],"over":[10],"a":[11,16,39,115,159],"network":[12],"of":[13,41,56,111,162],"nodes.":[14],"Integrating":[15],"technique":[17],"called":[18],"gradient":[19,24],"tracking":[20],"in":[21,144,152],"descent,":[25],"show":[27],"that":[28,68,80],"the":[29,60,70,76,91,96,102,108,130,133,147,163,166,179],"resulting":[30],"algorithm,":[31],"GT-DSGD,":[32],"enjoys":[33],"certain":[34],"desirable":[35],"characteristics":[36],"towards":[37],"minimizing":[38],"sum":[40],"smooth":[42,49],"functions.":[44],"particular,":[46],"for":[47,129],"general":[48],"functions,":[51],"establish":[53,107],"non-asymptotic":[54],"characterizations":[55],"GT-DSGD":[57,81,112],"and":[58,85,185],"derive":[59],"conditions":[61],"under":[62,123],"which":[63],"it":[64],"achieves":[65],"network-independent":[66],"performances":[67],"match":[69],"centralized":[71,92],"minibatch":[72,93],"SGD.":[73,94],"contrast,":[75],"existing":[77],"results":[78,170],"suggest":[79],"is":[82,86],"always":[83],"network-dependent":[84],"therefore":[87],"strictly":[88],"worse":[89],"than":[90],"When":[95],"global":[97,135],"function":[99],"additionally":[100],"satisfies":[101],"Polyak-\u0141ojasiewics":[103],"(PL)":[104],"condition,":[105,168],"linear":[109],"convergence":[110,137,183],"up":[113],"to":[114,146],"steady-state":[116],"error":[117],"with":[118],"appropriate":[119],"constant":[120],"step-sizes.":[121],"Moreover,":[122],"approximation":[125],"step-sizes,":[126],"establish,":[128],"first":[131],"time,":[132],"optimal":[134,149],"sublinear":[136,150],"rate":[138,151],"on":[139,188],"almost":[140],"every":[141],"sample":[142],"path,":[143],"addition":[145],"asymptotically":[148],"expectation.":[153],"Since":[154],"strongly":[155],"convex":[156],"functions":[157,164],"are":[158,171],"special":[160],"case":[161],"satisfying":[165],"PL":[167],"our":[169],"not":[172],"only":[173],"immediately":[174],"applicable":[175],"but":[176],"also":[177],"improve":[178],"currently":[180],"known":[181],"best":[182],"rates":[184],"their":[186],"dependence":[187],"problem":[189],"parameters.":[190]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":19},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2020-08-13T00:00:00"}