{"id":"https://openalex.org/W4313591116","doi":"https://doi.org/10.1109/tac.2023.3234176","title":"Global Convergence of Policy Gradient Primal\u2013Dual Methods for Risk-Constrained LQRs","display_name":"Global Convergence of Policy Gradient Primal\u2013Dual Methods for Risk-Constrained LQRs","publication_year":2023,"publication_date":"2023-01-04","ids":{"openalex":"https://openalex.org/W4313591116","doi":"https://doi.org/10.1109/tac.2023.3234176"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2023.3234176","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2023.3234176","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-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/A5026081309","display_name":"Feiran Zhao","orcid":"https://orcid.org/0000-0003-3142-2903"},"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":true,"raw_author_name":"Feiran Zhao","raw_affiliation_strings":["Department of Automation and BNRist, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation and BNRist, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088962631","display_name":"Keyou You","orcid":"https://orcid.org/0000-0003-4355-5340"},"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":"Keyou You","raw_affiliation_strings":["Department of Automation and BNRist, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Automation and BNRist, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019604570","display_name":"Tamer Ba\u015far","orcid":"https://orcid.org/0000-0003-4406-7875"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tamer Ba\u015far","raw_affiliation_strings":["Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026081309"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":5.9353,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.97028087,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"68","issue":"5","first_page":"2934","last_page":"2949"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9990000128746033,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9990000128746033,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9987000226974487,"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":0.9958000183105469,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6701705455780029},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6575800776481628},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5698108077049255},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.5647029280662537},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5326008200645447},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4977715313434601},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.45888739824295044},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44880157709121704},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.4246228337287903},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4220302700996399},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4194846749305725},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4190859794616699},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4181780219078064},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4109155833721161},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09582242369651794}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6701705455780029},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6575800776481628},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5698108077049255},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5647029280662537},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5326008200645447},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4977715313434601},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.45888739824295044},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44880157709121704},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.4246228337287903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4220302700996399},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4194846749305725},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4190859794616699},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4181780219078064},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4109155833721161},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09582242369651794},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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":1,"locations":[{"id":"doi:10.1109/tac.2023.3234176","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2023.3234176","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.44999998807907104,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1850434087","display_name":null,"funder_award_id":"62033006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W1518931405","https://openalex.org/W1841951819","https://openalex.org/W1981042292","https://openalex.org/W2020123437","https://openalex.org/W2070570138","https://openalex.org/W2096035449","https://openalex.org/W2098432798","https://openalex.org/W2121863487","https://openalex.org/W2128347943","https://openalex.org/W2145339207","https://openalex.org/W2155007355","https://openalex.org/W2161270100","https://openalex.org/W2178177313","https://openalex.org/W2416041116","https://openalex.org/W2583582904","https://openalex.org/W2804791273","https://openalex.org/W2822752092","https://openalex.org/W2886474253","https://openalex.org/W2901381232","https://openalex.org/W2904304778","https://openalex.org/W2963248893","https://openalex.org/W2963774238","https://openalex.org/W2963864421","https://openalex.org/W2967292964","https://openalex.org/W2972404875","https://openalex.org/W2981915592","https://openalex.org/W2991391803","https://openalex.org/W2995134936","https://openalex.org/W2998619042","https://openalex.org/W3046992251","https://openalex.org/W3098412154","https://openalex.org/W3101517963","https://openalex.org/W3118666236","https://openalex.org/W3141595720","https://openalex.org/W3162902207","https://openalex.org/W3176263050","https://openalex.org/W3206321238","https://openalex.org/W3209135762","https://openalex.org/W3213818741","https://openalex.org/W4226043618","https://openalex.org/W4250589301","https://openalex.org/W4254315244","https://openalex.org/W4281783469","https://openalex.org/W4293545785","https://openalex.org/W4297824337","https://openalex.org/W4304732000","https://openalex.org/W6682849425","https://openalex.org/W6684921986","https://openalex.org/W6687063787","https://openalex.org/W6726004062","https://openalex.org/W6733097720","https://openalex.org/W6737893269","https://openalex.org/W6751725685","https://openalex.org/W6754297394","https://openalex.org/W6756870468","https://openalex.org/W6766686101","https://openalex.org/W6767486501","https://openalex.org/W6770009701","https://openalex.org/W6772183843","https://openalex.org/W6785471904","https://openalex.org/W6797736639","https://openalex.org/W6802758289","https://openalex.org/W6838721327","https://openalex.org/W6846147899"],"related_works":["https://openalex.org/W2080941243","https://openalex.org/W3213165575","https://openalex.org/W4307261727","https://openalex.org/W2391797119","https://openalex.org/W2136200239","https://openalex.org/W2406638882","https://openalex.org/W4283709143","https://openalex.org/W2056178476","https://openalex.org/W2362763982","https://openalex.org/W4224273196"],"abstract_inverted_index":{"While":[0],"the":[1,10,17,48,55,89],"techniques":[2],"in":[3,123,136],"optimal":[4,79],"control":[5],"theory":[6],"are":[7],"often":[8],"model-based,":[9],"policy":[11,80,115],"optimization":[12,65],"(PO)":[13],"approach":[14,29],"directly":[15],"optimizes":[16],"performance":[18],"metric":[19],"of":[20,39,133],"interest.":[21],"Even":[22],"though":[23],"it":[24],"has":[25,81,99],"been":[26],"an":[27,78],"essential":[28],"for":[30],"reinforcement":[31],"learning":[32],"problems,":[33],"there":[34],"is":[35,93],"little":[36],"theoretical":[37],"understanding":[38],"its":[40],"performance.":[41],"In":[42],"this":[43],"article,":[44],"we":[45,70,108,113,130],"focus":[46],"on":[47,73,106],"risk-constrained":[49],"linear":[50],"quadratic":[51],"regulator":[52],"problem":[53],"via":[54],"PO":[56],"approach,":[57],"which":[58,107],"requires":[59],"addressing":[60],"a":[61,82,100],"challenging":[62],"nonconvex":[63],"constrained":[64],"problem.":[66],"To":[67],"solve":[68],"it,":[69],"first":[71],"build":[72],"our":[74,140],"earlier":[75],"result":[76],"that":[77,88],"time-invariant":[83],"affine":[84],"structure":[85],"to":[86,138],"show":[87],"associated":[90],"Lagrangian":[91],"function":[92],"coercive,":[94],"locally":[95],"gradient":[96,116],"dominated,":[97],"and":[98,126],"local":[101],"Lipschitz":[102],"continuous":[103],"gradient,":[104],"based":[105],"establish":[109],"strong":[110],"duality.":[111],"Then,":[112],"design":[114],"primal\u2013dual":[117],"methods":[118],"with":[119],"global":[120],"convergence":[121],"guarantees":[122],"both":[124],"model-based":[125],"sample-based":[127],"settings.":[128],"Finally,":[129],"use":[131],"samples":[132],"system":[134],"trajectories":[135],"simulations":[137],"validate":[139],"methods.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
