{"id":"https://openalex.org/W4391020115","doi":"https://doi.org/10.1109/cdc49753.2023.10383842","title":"Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding","display_name":"Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4391020115","doi":"https://doi.org/10.1109/cdc49753.2023.10383842"},"language":"en","primary_location":{"id":"doi:10.1109/cdc49753.2023.10383842","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10383842","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","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/A5055015446","display_name":"Tongzheng Ren","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tongzheng Ren","raw_affiliation_strings":["Google Brain and University of Texas,Austin","Google Brain and University of Texas, Austin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Brain and University of Texas,Austin","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"Google Brain and University of Texas, Austin","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050464562","display_name":"Zhaolin Ren","orcid":"https://orcid.org/0009-0006-6502-6430"},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhaolin Ren","raw_affiliation_strings":["Harvard University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harvard University","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100368048","display_name":"Na Li","orcid":"https://orcid.org/0000-0001-9545-3050"},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Na Li","raw_affiliation_strings":["Harvard University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harvard University","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086484914","display_name":"Bo Dai","orcid":"https://orcid.org/0000-0001-9448-8235"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]},{"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":"Bo Dai","raw_affiliation_strings":["Google Brain and Georgia Tech"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Brain and Georgia Tech","institution_ids":["https://openalex.org/I1291425158","https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7766,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70578488,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"795","last_page":"800"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9990000128746033,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9954000115394592,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6746180057525635},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6244069337844849},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6027018427848816},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5629783868789673},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.5414019823074341},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5021579265594482},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.501600980758667},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.49585065245628357},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4624137878417969},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45587533712387085},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.44663918018341064},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.4268863797187805},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.4112921357154846},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39470165967941284},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.13371187448501587},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10871383547782898},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07667273283004761}],"concepts":[{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6746180057525635},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6244069337844849},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6027018427848816},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5629783868789673},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.5414019823074341},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5021579265594482},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.501600980758667},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.49585065245628357},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4624137878417969},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45587533712387085},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.44663918018341064},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4268863797187805},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.4112921357154846},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39470165967941284},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.13371187448501587},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10871383547782898},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07667273283004761},{"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/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc49753.2023.10383842","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10383842","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.44999998807907104,"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1487127700","https://openalex.org/W1971902590","https://openalex.org/W1985054922","https://openalex.org/W1986280275","https://openalex.org/W1988505764","https://openalex.org/W1997054581","https://openalex.org/W2011014547","https://openalex.org/W2020282556","https://openalex.org/W2022638422","https://openalex.org/W2038730444","https://openalex.org/W2096394951","https://openalex.org/W2097467365","https://openalex.org/W2121523122","https://openalex.org/W2123395972","https://openalex.org/W2144902422","https://openalex.org/W2145763471","https://openalex.org/W2173810108","https://openalex.org/W2476606743","https://openalex.org/W2489939061","https://openalex.org/W2561027863","https://openalex.org/W2949361666","https://openalex.org/W2959895084","https://openalex.org/W3036251984","https://openalex.org/W3171210634","https://openalex.org/W4206212643","https://openalex.org/W4225912419","https://openalex.org/W4256152864","https://openalex.org/W4256153703","https://openalex.org/W4285483720","https://openalex.org/W4287135637","https://openalex.org/W4391020115","https://openalex.org/W6678945949","https://openalex.org/W6681302627","https://openalex.org/W6681439488","https://openalex.org/W6747473740","https://openalex.org/W6762918752","https://openalex.org/W6763329203","https://openalex.org/W6763711664","https://openalex.org/W6780349915","https://openalex.org/W6780486084","https://openalex.org/W6797672323","https://openalex.org/W6804503050","https://openalex.org/W6840436666","https://openalex.org/W6851604944"],"related_works":["https://openalex.org/W3048549205","https://openalex.org/W4399444697","https://openalex.org/W2173570290","https://openalex.org/W4306892756","https://openalex.org/W4389568284","https://openalex.org/W2995274466","https://openalex.org/W4386272992","https://openalex.org/W3120526207","https://openalex.org/W3153900688","https://openalex.org/W4301305831"],"abstract_inverted_index":{"Optimal":[0],"control":[1,49,69],"is":[2,58],"notoriously":[3],"difficult":[4],"for":[5,14,19,40],"stochastic":[6,67],"nonlinear":[7,68,74],"systems.":[8],"[1]":[9],"introduced":[10],"Spectral":[11,81],"Dynamics":[12,82],"Embedding":[13,83],"developing":[15],"reinforcement":[16],"learning":[17],"methods":[18,127,130],"controlling":[20],"an":[21,26,87],"unknown":[22],"system.":[23],"It":[24],"uses":[25],"infinite-dimensional":[27],"feature":[28,79],"to":[29,91],"linearly":[30],"represent":[31],"the":[32,44,56,73,77,93,98,119,123,132],"state-value":[33],"function":[34],"and":[35,101,112,121,128],"exploits":[36,72],"finite-dimensional":[37,45,78],"truncation":[38,100],"approximation":[39,46,94,107],"practical":[41],"implementation.":[42],"However,":[43],"properties":[47],"in":[48,108],"have":[50],"not":[51],"been":[52],"investigated":[53],"even":[54],"when":[55],"model":[57],"known.":[59],"In":[60],"this":[61],"paper,":[62],"we":[63],"provide":[64],"a":[65],"tractable":[66],"algorithm":[70,120],"that":[71],"dynamics":[75],"upon":[76],"approximation,":[80],"Control":[84],"(SDEC),":[85],"with":[86,125],"in-depth":[88],"theoretical":[89],"analysis":[90],"characterize":[92],"error":[95,103],"induced":[96,104],"by":[97,105],"finite-dimension":[99],"statistical":[102],"finite-sample":[106],"both":[109],"policy":[110,113],"evaluation":[111],"optimization.":[114],"We":[115],"also":[116],"empirically":[117],"test":[118],"compare":[122],"performance":[124],"Koopman-based":[126],"iLQR":[129],"on":[131],"pendulum":[133],"swingup":[134],"problem.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}