{"id":"https://openalex.org/W3110227966","doi":"https://doi.org/10.1109/tnnls.2021.3105227","title":"Training Generative Adversarial Networks via Stochastic Nash Games","display_name":"Training Generative Adversarial Networks via Stochastic Nash Games","publication_year":2021,"publication_date":"2021-08-26","ids":{"openalex":"https://openalex.org/W3110227966","doi":"https://doi.org/10.1109/tnnls.2021.3105227","mag":"3110227966","pmid":"https://pubmed.ncbi.nlm.nih.gov/34437077"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2021.3105227","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3105227","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2010.10013","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060370400","display_name":"Barbara Franci","orcid":"https://orcid.org/0000-0002-8298-0684"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Barbara Franci","raw_affiliation_strings":["Delft Center for System and Control, TU Delft, Delft, The Netherlands","[Delft Center for System and Control, TU Delft, Delft 2600AA, The Netherlands (e-mail: b.franci-1@tudelft.nl)]"],"raw_orcid":"https://orcid.org/0000-0002-8298-0684","affiliations":[{"raw_affiliation_string":"Delft Center for System and Control, TU Delft, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"[Delft Center for System and Control, TU Delft, Delft 2600AA, The Netherlands (e-mail: b.franci-1@tudelft.nl)]","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006692330","display_name":"Sergio Grammatico","orcid":"https://orcid.org/0000-0002-6021-2350"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Sergio Grammatico","raw_affiliation_strings":["Delft Center for System and Control, TU Delft, Delft, The Netherlands","(Delft University of Technology)"],"raw_orcid":"https://orcid.org/0000-0002-6021-2350","affiliations":[{"raw_affiliation_string":"Delft Center for System and Control, TU Delft, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"(Delft University of Technology)","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060370400"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":null,"apc_paid":null,"fwci":0.1942,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.45495969,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"34","issue":"3","first_page":"1319","last_page":"1328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9984999895095825,"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/convergence","display_name":"Convergence (economics)","score":0.6970604062080383},{"id":"https://openalex.org/keywords/discriminator","display_name":"Discriminator","score":0.6787573099136353},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6697635650634766},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.6508485674858093},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6285606026649475},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.544165849685669},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.536666750907898},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5198981761932373},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.49858808517456055},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4512641727924347},{"id":"https://openalex.org/keywords/adversarial-system","display_name":"Adversarial system","score":0.44362539052963257},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.43770378828048706},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4174421727657318},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4162366986274719},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3263414800167084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2595342993736267}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6970604062080383},{"id":"https://openalex.org/C2779803651","wikidata":"https://www.wikidata.org/wiki/Q5282088","display_name":"Discriminator","level":3,"score":0.6787573099136353},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6697635650634766},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.6508485674858093},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6285606026649475},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.544165849685669},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.536666750907898},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5198981761932373},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.49858808517456055},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4512641727924347},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.44362539052963257},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.43770378828048706},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4174421727657318},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4162366986274719},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3263414800167084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2595342993736267},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","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}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/tnnls.2021.3105227","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3105227","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:34437077","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34437077","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null},{"id":"pmh:oai:arXiv.org:2010.10013","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.10013","pdf_url":"https://arxiv.org/pdf/2010.10013","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":"","raw_type":"text"},{"id":"pmh:tud:oai:tudelft.nl:uuid:6de8ebab-7dc1-4a81-bac7-323e53db9592","is_oa":true,"landing_page_url":"http://resolver.tudelft.nl/uuid:6de8ebab-7dc1-4a81-bac7-323e53db9592","pdf_url":"https://repository.tudelft.nl/file/File_9af53a32-8e4c-4e5e-a8b5-0001e6f21151","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems, 34(3)","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:3110227966","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2010.10013","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2010.10013","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2010.10013","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2010.10013","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.10013","pdf_url":"https://arxiv.org/pdf/2010.10013","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":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.7400000095367432,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1608658613","display_name":null,"funder_award_id":"647.003.003","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5457097406","display_name":null,"funder_award_id":"613.001.702","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G8620738847","display_name":null,"funder_award_id":"802348","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1519983590","https://openalex.org/W1522301498","https://openalex.org/W1543439990","https://openalex.org/W1977794212","https://openalex.org/W1994616650","https://openalex.org/W2008796819","https://openalex.org/W2015320990","https://openalex.org/W2028148084","https://openalex.org/W2052769657","https://openalex.org/W2055467852","https://openalex.org/W2055828890","https://openalex.org/W2061627126","https://openalex.org/W2099471712","https://openalex.org/W2173520492","https://openalex.org/W2432004435","https://openalex.org/W2479004360","https://openalex.org/W2497446532","https://openalex.org/W2577946330","https://openalex.org/W2593248927","https://openalex.org/W2743780012","https://openalex.org/W2755577605","https://openalex.org/W2771120189","https://openalex.org/W2788053000","https://openalex.org/W2808305757","https://openalex.org/W2888709019","https://openalex.org/W2921478860","https://openalex.org/W2932550525","https://openalex.org/W2951567597","https://openalex.org/W2953030256","https://openalex.org/W2953354794","https://openalex.org/W2963017889","https://openalex.org/W2963981733","https://openalex.org/W2965900084","https://openalex.org/W2992581314","https://openalex.org/W3004056434","https://openalex.org/W3006882295","https://openalex.org/W3007954193","https://openalex.org/W3010808375","https://openalex.org/W3014151993","https://openalex.org/W3035191209","https://openalex.org/W3037777342","https://openalex.org/W3041579012","https://openalex.org/W3045167173","https://openalex.org/W3085615344","https://openalex.org/W3096831136","https://openalex.org/W3105389099","https://openalex.org/W3105688066","https://openalex.org/W3115439033","https://openalex.org/W3118608800","https://openalex.org/W3119296055","https://openalex.org/W3122435563","https://openalex.org/W3127284993","https://openalex.org/W3176880348","https://openalex.org/W3180849732","https://openalex.org/W4229650096","https://openalex.org/W6631077220","https://openalex.org/W6631190155","https://openalex.org/W6685352114","https://openalex.org/W6718379498","https://openalex.org/W6738546315","https://openalex.org/W6746914671","https://openalex.org/W6748541206","https://openalex.org/W6749927861","https://openalex.org/W6755219850","https://openalex.org/W6763060542","https://openalex.org/W6765779288","https://openalex.org/W6774381916","https://openalex.org/W6774766356","https://openalex.org/W6779669310","https://openalex.org/W6787972765"],"related_works":["https://openalex.org/W3193785335","https://openalex.org/W3119296055","https://openalex.org/W2845818548","https://openalex.org/W3082580287","https://openalex.org/W3005217928","https://openalex.org/W3195418377","https://openalex.org/W3014967337","https://openalex.org/W2964098908","https://openalex.org/W3112730052","https://openalex.org/W1842998987","https://openalex.org/W3093099641","https://openalex.org/W2786479217","https://openalex.org/W2172183234","https://openalex.org/W2941095974","https://openalex.org/W2964381205","https://openalex.org/W2964247959","https://openalex.org/W2964039732","https://openalex.org/W2567844727","https://openalex.org/W2570547546","https://openalex.org/W2180467047"],"abstract_inverted_index":{"Generative":[0],"adversarial":[1,30],"networks":[2,23],"(GANs)":[3],"are":[4,112],"a":[5,15,18,37,65,102,109],"class":[6],"of":[7,85,93,97,104,124],"generative":[8],"models":[9],"with":[10],"two":[11,21],"antagonistic":[12],"neural":[13,22],"networks:":[14],"generator":[16],"and":[17,73],"discriminator.":[19],"These":[20],"compete":[24],"against":[25],"each":[26],"other":[27],"through":[28],"an":[29,58,78,82,94],"process":[31,46],"that":[32],"can":[33],"be":[34],"modeled":[35],"as":[36],"stochastic":[38,66],"Nash":[39],"equilibrium":[40],"problem.":[41,148],"Since":[42],"the":[43,98,105,121,125,133,137,145],"associated":[44],"training":[45],"is":[47,50,87,118,127,131],"challenging,":[48],"it":[49],"fundamental":[51],"to":[52,56,77,101,144],"design":[53],"reliable":[54],"algorithms":[55],"compute":[57],"equilibrium.":[59],"In":[60,114],"this":[61],"article,":[62],"we":[63,74,140],"propose":[64],"relaxed":[67],"forward-backward":[68],"(SRFB)":[69],"algorithm":[70,100,143],"for":[71],"GANs,":[72],"show":[75,91],"convergence":[76,92,117],"exact":[79],"solution":[80,106],"when":[81,107,120],"increasing":[83],"number":[84],"data":[86],"available.":[88,113],"We":[89],"also":[90],"averaged":[95],"variant":[96],"SRFB":[99],"neighborhood":[103],"only":[108],"few":[110],"samples":[111],"both":[115],"cases,":[116],"guaranteed":[119],"pseudogradient":[122],"mapping":[123],"game":[126],"monotone.":[128],"This":[129],"assumption":[130],"among":[132],"weakest":[134],"known":[135],"in":[136],"literature.":[138],"Moreover,":[139],"apply":[141],"our":[142],"image":[146],"generation":[147]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}