{"id":"https://openalex.org/W4387965994","doi":"https://doi.org/10.1109/tcyb.2023.3323316","title":"Optimization Landscape of Policy Gradient Methods for Discrete-Time Static Output Feedback","display_name":"Optimization Landscape of Policy Gradient Methods for Discrete-Time Static Output Feedback","publication_year":2023,"publication_date":"2023-10-26","ids":{"openalex":"https://openalex.org/W4387965994","doi":"https://doi.org/10.1109/tcyb.2023.3323316","pmid":"https://pubmed.ncbi.nlm.nih.gov/37883283"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2023.3323316","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2023.3323316","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2310.19022","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067909017","display_name":"Jingliang Duan","orcid":"https://orcid.org/0000-0002-3697-1576"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN","SG"],"is_corresponding":true,"raw_author_name":"Jingliang Duan","raw_affiliation_strings":["School of Mechanical Engineering, University of Science and Technology Beijing, Beijing, China","Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-3697-1576","affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100696317","display_name":"Jie Li","orcid":"https://orcid.org/0000-0002-3718-5593"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Li","raw_affiliation_strings":["School of Vehicle and Mobility, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-3718-5593","affiliations":[{"raw_affiliation_string":"School of Vehicle and Mobility, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057914336","display_name":"Xuyang Chen","orcid":"https://orcid.org/0000-0002-1050-1285"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Xuyang Chen","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Queenstown, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-1050-1285","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Queenstown, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061456453","display_name":"Kai Zhao","orcid":"https://orcid.org/0000-0003-0656-1901"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Kai Zhao","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Queenstown, Singapore"],"raw_orcid":"https://orcid.org/0000-0003-0656-1901","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Queenstown, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100747108","display_name":"Shengbo Eben Li","orcid":"https://orcid.org/0000-0003-4923-3633"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shengbo Eben Li","raw_affiliation_strings":["School of Vehicle and Mobility, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-4923-3633","affiliations":[{"raw_affiliation_string":"School of Vehicle and Mobility, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064240573","display_name":"Lin Zhao","orcid":"https://orcid.org/0000-0002-1078-887X"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Lin Zhao","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Queenstown, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-1078-887X","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Queenstown, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5067909017"],"corresponding_institution_ids":["https://openalex.org/I165932596","https://openalex.org/I92403157"],"apc_list":null,"apc_paid":null,"fwci":1.5518,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.8593667,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"54","issue":"6","first_page":"3588","last_page":"3601"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9700000286102295,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9646000266075134,"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/hessian-matrix","display_name":"Hessian matrix","score":0.6428984999656677},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5625287890434265},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5476183295249939},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5327356457710266},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.5259433388710022},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.4856623411178589},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4822548031806946},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4729708731174469},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.41664111614227295},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3767353296279907},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35607069730758667},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.25716090202331543},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.14443182945251465},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10932007431983948},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.09459793567657471},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.0862019956111908}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6428984999656677},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5625287890434265},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5476183295249939},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5327356457710266},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.5259433388710022},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.4856623411178589},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4822548031806946},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4729708731174469},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.41664111614227295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3767353296279907},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35607069730758667},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.25716090202331543},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.14443182945251465},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10932007431983948},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.09459793567657471},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0862019956111908},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tcyb.2023.3323316","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2023.3323316","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:37883283","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37883283","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 cybernetics","raw_type":null},{"id":"pmh:oai:arXiv.org:2310.19022","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.19022","pdf_url":"https://arxiv.org/pdf/2310.19022","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:2310.19022","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.19022","pdf_url":"https://arxiv.org/pdf/2310.19022","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":[{"id":"https://metadata.un.org/sdg/16","score":0.4399999976158142,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1254682421","display_name":null,"funder_award_id":"52202487","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8491981559","display_name":null,"funder_award_id":"KFY2212","funder_id":"https://openalex.org/F4320326925","funder_display_name":"State Key Laboratory of Automotive Safety and Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320326925","display_name":"State Key Laboratory of Automotive Safety and Energy","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387965994.pdf","grobid_xml":"https://content.openalex.org/works/W4387965994.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W181733065","https://openalex.org/W1590099731","https://openalex.org/W2107093743","https://openalex.org/W2149479912","https://openalex.org/W2161367843","https://openalex.org/W2546420264","https://openalex.org/W2589578140","https://openalex.org/W2903410452","https://openalex.org/W2938668169","https://openalex.org/W2963774238","https://openalex.org/W3011908139","https://openalex.org/W3015082424","https://openalex.org/W3087319130","https://openalex.org/W3108352764","https://openalex.org/W3109546547","https://openalex.org/W3185181536","https://openalex.org/W3203485495","https://openalex.org/W3204571453","https://openalex.org/W3205519146","https://openalex.org/W3206480318","https://openalex.org/W3209135762","https://openalex.org/W4205172873","https://openalex.org/W4205939747","https://openalex.org/W4224216677","https://openalex.org/W4226090675","https://openalex.org/W4226245271","https://openalex.org/W4229650096","https://openalex.org/W4291910408","https://openalex.org/W4293195488","https://openalex.org/W4310330864","https://openalex.org/W4320473289","https://openalex.org/W4323897042","https://openalex.org/W4362650413","https://openalex.org/W4376481351","https://openalex.org/W6637461557","https://openalex.org/W6679257226","https://openalex.org/W6684921986","https://openalex.org/W6734280532","https://openalex.org/W6747473740","https://openalex.org/W6754297394","https://openalex.org/W6756870468","https://openalex.org/W6761170661","https://openalex.org/W6763002318","https://openalex.org/W6766686101","https://openalex.org/W6772183843","https://openalex.org/W6791005554","https://openalex.org/W6797736639","https://openalex.org/W6922480057"],"related_works":["https://openalex.org/W4243698225","https://openalex.org/W2947416323","https://openalex.org/W4288346661","https://openalex.org/W4297883503","https://openalex.org/W2744293077","https://openalex.org/W2355987247","https://openalex.org/W263682811","https://openalex.org/W2846499288","https://openalex.org/W2564172750","https://openalex.org/W2082542187"],"abstract_inverted_index":{"In":[0],"recent":[1],"times,":[2],"significant":[3],"advancements":[4],"have":[5],"been":[6],"made":[7],"in":[8,22,48,71],"delving":[9],"into":[10,192],"the":[11,37,41,55,86,99,126,131,137,145,178,185,193,201],"optimization":[12,56],"landscape":[13,57],"of":[14,40,85,101,180,195,203],"policy":[15,60,122,128,133,147,197],"gradient":[16,61,123,129,134,148,181,198],"methods":[17,62,199],"for":[18,120,183],"achieving":[19],"optimal":[20],"control":[21,32,70],"linear":[23,151],"time-invariant":[24],"(LTI)":[25],"systems.":[26],"Compared":[27],"with":[28],"state-feedback":[29],"control,":[30],"output-feedback":[31],"is":[33],"more":[34],"prevalent":[35],"since":[36],"underlying":[38],"state":[39],"system":[42],"may":[43],"not":[44,175],"be":[45],"fully":[46],"observed":[47],"many":[49],"practical":[50],"settings.":[51],"This":[52,161],"article":[53,162],"analyzes":[54],"inherent":[58],"to":[59,65,76,107,117],"when":[63,156],"applied":[64],"static":[66],"output":[67],"feedback":[68],"(SOF)":[69],"discrete-time":[72],"LTI":[73],"systems":[74],"subject":[75],"quadratic":[77],"cost.":[78],"We":[79],"begin":[80],"by":[81,164],"establishing":[82],"crucial":[83],"properties":[84,106],"SOF":[87,186],"cost,":[88],"encompassing":[89],"coercivity,":[90],"L":[91],"-smoothness,":[92],"and":[93,136],"M":[94],"-Lipschitz":[95],"continuous":[96],"Hessian.":[97],"Despite":[98],"absence":[100],"convexity,":[102],"we":[103,141],"leverage":[104],"these":[105],"derive":[108],"novel":[109],"findings":[110],"regarding":[111],"convergence":[112,152],"(and":[113],"nearly":[114],"dimension-free":[115],"rate)":[116],"stationary":[118],"points":[119],"three":[121],"methods,":[124],"including":[125],"vanilla":[127,146],"method,":[130,135],"natural":[132],"Gauss-Newton":[138],"method.":[139],"Moreover,":[140],"provide":[142,190],"proof":[143],"that":[144,168],"method":[149],"exhibits":[150],"toward":[153],"local":[154],"minima":[155],"initialized":[157],"near":[158],"such":[159],"minima.":[160],"concludes":[163],"presenting":[165],"numerical":[166],"examples":[167],"validate":[169],"our":[170],"theoretical":[171],"findings.":[172],"These":[173],"results":[174],"only":[176],"characterize":[177],"performance":[179],"descent":[182],"optimizing":[184],"problem":[187],"but":[188],"also":[189],"insights":[191],"effectiveness":[194],"general":[196],"within":[200],"realm":[202],"reinforcement":[204],"learning.":[205]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
