{"id":"https://openalex.org/W2965895369","doi":"https://doi.org/10.24963/ijcai.2019/556","title":"On the Convergence of (Stochastic) Gradient Descent with Extrapolation for Non-Convex Minimization","display_name":"On the Convergence of (Stochastic) Gradient Descent with Extrapolation for Non-Convex Minimization","publication_year":2019,"publication_date":"2019-07-28","ids":{"openalex":"https://openalex.org/W2965895369","doi":"https://doi.org/10.24963/ijcai.2019/556","mag":"2965895369"},"language":"en","primary_location":{"id":"doi:10.24963/ijcai.2019/556","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2019/556","pdf_url":"https://www.ijcai.org/proceedings/2019/0556.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.ijcai.org/proceedings/2019/0556.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018343158","display_name":"Yi Xu","orcid":"https://orcid.org/0000-0003-2126-6054"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yi Xu","raw_affiliation_strings":["The University of Iowa"],"affiliations":[{"raw_affiliation_string":"The University of Iowa","institution_ids":["https://openalex.org/I126307644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101782099","display_name":"Zhuoning Yuan","orcid":"https://orcid.org/0009-0009-9364-2486"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhuoning Yuan","raw_affiliation_strings":["The University of Iowa"],"affiliations":[{"raw_affiliation_string":"The University of Iowa","institution_ids":["https://openalex.org/I126307644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002854172","display_name":"Sen Yang","orcid":"https://orcid.org/0000-0003-3222-2268"},"institutions":[{"id":"https://openalex.org/I4210095624","display_name":"Alibaba Group (United States)","ror":"https://ror.org/00rn0m335","country_code":"US","type":"company","lineage":["https://openalex.org/I4210095624","https://openalex.org/I45928872"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sen Yang","raw_affiliation_strings":["Alibaba Group","Alibaba Group {yi-xu, zhuoning-"],"affiliations":[{"raw_affiliation_string":"Alibaba Group","institution_ids":["https://openalex.org/I4210095624"]},{"raw_affiliation_string":"Alibaba Group {yi-xu, zhuoning-","institution_ids":["https://openalex.org/I4210095624"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101873437","display_name":"Rong Jin","orcid":"https://orcid.org/0000-0003-1789-236X"},"institutions":[{"id":"https://openalex.org/I4210095624","display_name":"Alibaba Group (United States)","ror":"https://ror.org/00rn0m335","country_code":"US","type":"company","lineage":["https://openalex.org/I4210095624","https://openalex.org/I45928872"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rong Jin","raw_affiliation_strings":["Alibaba Group","Alibaba Group {yi-xu, zhuoning-"],"affiliations":[{"raw_affiliation_string":"Alibaba Group","institution_ids":["https://openalex.org/I4210095624"]},{"raw_affiliation_string":"Alibaba Group {yi-xu, zhuoning-","institution_ids":["https://openalex.org/I4210095624"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023288846","display_name":"Tianbao Yang","orcid":"https://orcid.org/0000-0002-7858-5438"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tianbao Yang","raw_affiliation_strings":["The University of Iowa"],"affiliations":[{"raw_affiliation_string":"The University of Iowa","institution_ids":["https://openalex.org/I126307644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5018343158"],"corresponding_institution_ids":["https://openalex.org/I126307644"],"apc_list":null,"apc_paid":null,"fwci":0.578,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75760757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"4003","last_page":"4009"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9812999963760376,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/extrapolation","display_name":"Extrapolation","score":0.9497249722480774},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.7487733960151672},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6621294021606445},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.6363709568977356},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5566608309745789},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5228174924850464},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5215301513671875},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5153988599777222},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.515105664730072},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.49014243483543396},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4739173352718353},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4632744789123535},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4271451532840729},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.4223173260688782},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3560805320739746},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18803507089614868},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11159023642539978},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.07958012819290161},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04929199814796448}],"concepts":[{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.9497249722480774},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.7487733960151672},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6621294021606445},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.6363709568977356},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5566608309745789},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5228174924850464},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5215301513671875},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5153988599777222},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.515105664730072},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.49014243483543396},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4739173352718353},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4632744789123535},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4271451532840729},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.4223173260688782},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3560805320739746},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18803507089614868},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11159023642539978},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.07958012819290161},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04929199814796448},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.24963/ijcai.2019/556","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2019/556","pdf_url":"https://www.ijcai.org/proceedings/2019/0556.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.24963/ijcai.2019/556","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2019/556","pdf_url":"https://www.ijcai.org/proceedings/2019/0556.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4099999964237213,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G7902954316","display_name":null,"funder_award_id":"1545995","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2965895369.pdf","grobid_xml":"https://content.openalex.org/works/W2965895369.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1487404723","https://openalex.org/W1987083649","https://openalex.org/W1998544309","https://openalex.org/W2029463628","https://openalex.org/W2043093325","https://openalex.org/W2088253680","https://openalex.org/W2089559088","https://openalex.org/W2093417350","https://openalex.org/W2106005123","https://openalex.org/W2110412969","https://openalex.org/W2134829400","https://openalex.org/W2158460069","https://openalex.org/W2186453173","https://openalex.org/W2788053000","https://openalex.org/W2808402975","https://openalex.org/W2833268639","https://openalex.org/W2895969815","https://openalex.org/W2936995161","https://openalex.org/W2962826994","https://openalex.org/W2963190258","https://openalex.org/W2963470657","https://openalex.org/W2963625269","https://openalex.org/W2963837252","https://openalex.org/W4299041948"],"related_works":["https://openalex.org/W2170262790","https://openalex.org/W4387882783","https://openalex.org/W4384613829","https://openalex.org/W2944517508","https://openalex.org/W2804400349","https://openalex.org/W2182021692","https://openalex.org/W4297153560","https://openalex.org/W2964186284","https://openalex.org/W25321933","https://openalex.org/W4224283687"],"abstract_inverted_index":{"Extrapolation":[0],"is":[1],"a":[2,46],"well-known":[3],"technique":[4],"for":[5,17,39,67],"solving":[6],"convex":[7],"optimization":[8,77],"and":[9,12,42,51,61],"variational":[10],"inequalities":[11],"recently":[13],"attracts":[14],"some":[15,29],"attention":[16],"non-convex":[18,40,76],"optimization.":[19],"Several":[20],"recent":[21],"works":[22],"have":[23],"empirically":[24],"shown":[25],"its":[26],"success":[27],"in":[28,74],"machine":[30],"learning":[31],"tasks.":[32],"However,":[33],"it":[34],"has":[35],"not":[36],"been":[37],"analyzed":[38],"minimization":[41],"there":[43],"still":[44],"remains":[45],"gap":[47],"between":[48],"the":[49,52,85],"theory":[50],"practice.":[53],"In":[54],"this":[55],"paper,":[56],"we":[57],"analyze":[58],"gradient":[59,63],"descent":[60,64],"stochastic":[62],"with":[65,87],"extrapolation":[66,88],"finding":[68],"an":[69],"approximate":[70],"first-order":[71],"stationary":[72],"point":[73],"smooth":[75],"problems.":[78],"Our":[79],"convergence":[80],"upper":[81],"bounds":[82],"show":[83],"that":[84],"algorithms":[86],"can":[89],"be":[90],"accelerated":[91],"than":[92],"without":[93],"extrapolation.":[94]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}