{"id":"https://openalex.org/W3013634249","doi":"https://doi.org/10.1109/ieeeconf44664.2019.9048943","title":"Alternating Gradient Descent Ascent for Nonconvex Min-Max Problems in Robust Learning and GANs","display_name":"Alternating Gradient Descent Ascent for Nonconvex Min-Max Problems in Robust Learning and GANs","publication_year":2019,"publication_date":"2019-11-01","ids":{"openalex":"https://openalex.org/W3013634249","doi":"https://doi.org/10.1109/ieeeconf44664.2019.9048943","mag":"3013634249"},"language":"en","primary_location":{"id":"doi:10.1109/ieeeconf44664.2019.9048943","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ieeeconf44664.2019.9048943","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 53rd Asilomar Conference on Signals, Systems, and Computers","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/A5088593720","display_name":"Songtao Lu","orcid":"https://orcid.org/0000-0001-9256-9648"},"institutions":[{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Songtao Lu","raw_affiliation_strings":["IBM Thomas J. Watson Research Center, IBM Research AI, New York, USA","IBM Research AI,IBM Thomas J. Watson Research Center,New York,USA,10598"],"affiliations":[{"raw_affiliation_string":"IBM Thomas J. Watson Research Center, IBM Research AI, New York, USA","institution_ids":["https://openalex.org/I4210114115"]},{"raw_affiliation_string":"IBM Research AI,IBM Thomas J. Watson Research Center,New York,USA,10598","institution_ids":["https://openalex.org/I4210114115"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101901792","display_name":"Rahul Singh","orcid":"https://orcid.org/0000-0002-3889-8456"},"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":"Rahul Singh","raw_affiliation_strings":["School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA","Georgia Institute of Technology,School of Aerospace Engineering,Atlanta,GA,USA,30332"],"affiliations":[{"raw_affiliation_string":"School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Georgia Institute of Technology,School of Aerospace Engineering,Atlanta,GA,USA,30332","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049896980","display_name":"Xiangyi Chen","orcid":"https://orcid.org/0000-0001-5549-5336"},"institutions":[{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]},{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiangyi Chen","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota Twin Cities, Minneapolis, MN, USA","University of Minnesota Twin Cities,Department of Electrical and Computer Engineering,Minneapolis,MN,USA,55455"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota Twin Cities, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]},{"raw_affiliation_string":"University of Minnesota Twin Cities,Department of Electrical and Computer Engineering,Minneapolis,MN,USA,55455","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066940107","display_name":"Yongxin Chen","orcid":"https://orcid.org/0000-0002-1459-6365"},"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":"Yongxin Chen","raw_affiliation_strings":["School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA","Georgia Institute of Technology,School of Aerospace Engineering,Atlanta,GA,USA,30332"],"affiliations":[{"raw_affiliation_string":"School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Georgia Institute of Technology,School of Aerospace Engineering,Atlanta,GA,USA,30332","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100633783","display_name":"Mingyi Hong","orcid":"https://orcid.org/0000-0003-1263-9365"},"institutions":[{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]},{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mingyi Hong","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota Twin Cities, Minneapolis, MN, USA","University of Minnesota Twin Cities,Department of Electrical and Computer Engineering,Minneapolis,MN,USA,55455"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota Twin Cities, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]},{"raw_affiliation_string":"University of Minnesota Twin Cities,Department of Electrical and Computer Engineering,Minneapolis,MN,USA,55455","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5088593720"],"corresponding_institution_ids":["https://openalex.org/I4210114115"],"apc_list":null,"apc_paid":null,"fwci":0.3783,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61527275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"680","last_page":"684"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998000264167786,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9965999722480774,"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/sublinear-function","display_name":"Sublinear function","score":0.841616153717041},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6185522675514221},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5940989851951599},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5589594841003418},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.5266261696815491},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5254456400871277},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5222283601760864},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5189914107322693},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5064386129379272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.497974157333374},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4811733663082123},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47406381368637085},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.42944759130477905},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42022061347961426},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40418541431427},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23412832617759705},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1577867865562439},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.08895093202590942},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07130059599876404}],"concepts":[{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.841616153717041},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6185522675514221},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5940989851951599},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5589594841003418},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.5266261696815491},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5254456400871277},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5222283601760864},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5189914107322693},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5064386129379272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.497974157333374},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4811733663082123},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47406381368637085},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.42944759130477905},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42022061347961426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40418541431427},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23412832617759705},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1577867865562439},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.08895093202590942},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07130059599876404},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ieeeconf44664.2019.9048943","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ieeeconf44664.2019.9048943","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 53rd Asilomar Conference on Signals, Systems, and Computers","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":41,"referenced_works":["https://openalex.org/W2092851214","https://openalex.org/W2099471712","https://openalex.org/W2112796928","https://openalex.org/W2163605009","https://openalex.org/W2173520492","https://openalex.org/W2564590721","https://openalex.org/W2619503996","https://openalex.org/W2765094320","https://openalex.org/W2766210095","https://openalex.org/W2791323206","https://openalex.org/W2803117117","https://openalex.org/W2890485411","https://openalex.org/W2895628298","https://openalex.org/W2953259620","https://openalex.org/W2963049063","https://openalex.org/W2963508732","https://openalex.org/W2963684088","https://openalex.org/W2964018346","https://openalex.org/W2964126461","https://openalex.org/W2964253222","https://openalex.org/W2964334726","https://openalex.org/W3016604587","https://openalex.org/W4293846201","https://openalex.org/W4297807263","https://openalex.org/W4297944735","https://openalex.org/W4320013936","https://openalex.org/W6684191040","https://openalex.org/W6685352114","https://openalex.org/W6730898090","https://openalex.org/W6738546315","https://openalex.org/W6738677829","https://openalex.org/W6739448629","https://openalex.org/W6739868092","https://openalex.org/W6744644060","https://openalex.org/W6745905863","https://openalex.org/W6749133739","https://openalex.org/W6751249977","https://openalex.org/W6754637010","https://openalex.org/W6754803017","https://openalex.org/W6776078682","https://openalex.org/W6779669310"],"related_works":["https://openalex.org/W9059077","https://openalex.org/W39176023","https://openalex.org/W3022588902","https://openalex.org/W1985812215","https://openalex.org/W2111200844","https://openalex.org/W2789199296","https://openalex.org/W4389767465","https://openalex.org/W2950674002","https://openalex.org/W2054621035","https://openalex.org/W2978731891"],"abstract_inverted_index":{"We":[0,148,184],"study":[1],"a":[2,134,141,152,156,168,172],"class":[3,23,143],"of":[4,24,104,107,144,197],"nonconvex-strongly-concave":[5,145],"min-max":[6,99,146],"optimization":[7],"problems.":[8,86,147,201],"A":[9],"most":[10],"commonly":[11],"used":[12],"algorithm":[13,162],"for":[14],"such":[15],"problems":[16,77],"in":[17,38,45,164],"machine":[18,199],"learning":[19,200],"applications":[20],"is":[21,69,72,88,180],"the":[22,66,102,119,125,181,194],"first-order":[25,108],"algorithms":[26],"where":[27,78,178],"gradient":[28,159],"descent":[29],"and":[30,121,127],"ascent":[31],"steps":[32],"are":[33,50,81,112],"performed":[34],"simultaneously":[35],"or":[36],"alternatively":[37],"each":[39],"step.":[40],"Despite":[41,101],"its":[42,47,63,110],"great":[43],"success":[44],"practice,":[46],"theoretical":[48,195],"properties":[49,111,196],"far":[51],"from":[52,75],"being":[53],"understood.":[54],"In":[55],"fact,":[56,165],"not":[57,89],"much":[58],"has":[59],"been":[60],"said":[61],"about":[62],"convergence":[64],"once":[65],"convex-concave":[67],"assumption":[68],"absent.":[70],"This":[71],"considerably":[73],"different":[74],"minimization":[76,128],"many":[79],"techniques":[80,94],"available":[82],"to":[83,98,115,118,167],"analyze":[84,116],"nonconvex":[85,122],"It":[87],"clear":[90],"that":[91],"if":[92],"these":[93],"can":[95],"be":[96],"applied":[97],"optimization.":[100],"simplicity":[103],"this":[105,130,137],"type":[106],"methods,":[109],"extremely":[113],"difficult":[114],"due":[117],"nonlinear":[120],"coupling":[123],"between":[124],"maximization":[126],"steps.(p)(/p)In":[129],"paper,":[131],"we":[132],"take":[133],"step":[135],"toward":[136],"direction":[138],"by":[139],"examining":[140],"special":[142],"show":[149],"that,":[150],"with":[151,171],"proper":[153],"stepsize":[154],"choice,":[155],"simple":[157],"alternating":[158],"descent/ascent":[160],"(AGDA)":[161],"would,":[163],"converge":[166],"stationary":[169],"solution":[170],"sublinear":[173],"rate":[174],"$\\mathcal{O}\\left(":[175],"{1/t}":[176],"\\right)$,":[177],"t":[179],"iteration":[182],"number.":[183],"hope":[185],"our":[186],"analysis":[187],"sheds":[188],"light":[189],"on":[190,193],"future":[191],"studies":[192],"relevant":[198]},"counts_by_year":[{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
