{"id":"https://openalex.org/W2165418472","doi":"https://doi.org/10.1109/tac.2009.2022097","title":"Convergence Results for Some Temporal Difference Methods Based on Least Squares","display_name":"Convergence Results for Some Temporal Difference Methods Based on Least Squares","publication_year":2009,"publication_date":"2009-07-01","ids":{"openalex":"https://openalex.org/W2165418472","doi":"https://doi.org/10.1109/tac.2009.2022097","mag":"2165418472"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2009.2022097","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2009.2022097","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/1721.1/74102","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014937312","display_name":"Huizhen Yu","orcid":"https://orcid.org/0000-0002-3673-0094"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]},{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]}],"countries":["FI","US"],"is_corresponding":false,"raw_author_name":"Huizhen Yu","raw_affiliation_strings":["Department of Computer Science and HIIT, University of Helsinki, Helsinki, Finland","Laboratory of Information and Decision Systems LIDS, M I T, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and HIIT, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052"]},{"raw_affiliation_string":"Laboratory of Information and Decision Systems LIDS, M I T, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210143601"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039911471","display_name":"Dimitri P. Bertsekas","orcid":"https://orcid.org/0000-0001-6909-7208"},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D.P. Bertsekas","raw_affiliation_strings":["Laboratory of Information and Decision Systems LIDS, Massachusetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Information and Decision Systems LIDS, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":16.9425,"has_fulltext":false,"cited_by_count":102,"citation_normalized_percentile":{"value":0.9910635,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"54","issue":"7","first_page":"1515","last_page":"1531"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9984999895095825,"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/T12288","display_name":"Optimization and Search Problems","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11195","display_name":"Simulation Techniques and Applications","score":0.9944000244140625,"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/convergence","display_name":"Convergence (economics)","score":0.690269410610199},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6800981163978577},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6250226497650146},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5791449546813965},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.5514534115791321},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.547814667224884},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5059811472892761},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.48905929923057556},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.47714897990226746},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4300232231616974},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.42449820041656494},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.4117424786090851},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.33128494024276733},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2300887107849121},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13605186343193054},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.06484672427177429}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.690269410610199},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6800981163978577},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6250226497650146},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5791449546813965},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.5514534115791321},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.547814667224884},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5059811472892761},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.48905929923057556},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.47714897990226746},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4300232231616974},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.42449820041656494},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.4117424786090851},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.33128494024276733},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2300887107849121},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13605186343193054},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.06484672427177429},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tac.2009.2022097","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2009.2022097","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.151.6005","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.151.6005","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.mit.edu/dimitrib/www/lspe_lids_final.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.294.8786","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.294.8786","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.mit.edu/dimitrib/www/lspe_ieee_final.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.62.4302","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.4302","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-mit.mit.edu/dimitrib/www/lspe.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.mit.edu:1721.1/74102","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/74102","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/74102","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/74102","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE","raw_type":"http://purl.org/eprint/type/JournalArticle"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7799999713897705,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G5819659178","display_name":"ITR: Optimal and Suboptimal Routing and Wavelength Assignment in Optical and Circuit Switched Networks","funder_award_id":"0218328","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1499021337","https://openalex.org/W1507222174","https://openalex.org/W1518539242","https://openalex.org/W1553320709","https://openalex.org/W1576452626","https://openalex.org/W1583072328","https://openalex.org/W1597303641","https://openalex.org/W1966221033","https://openalex.org/W1997394097","https://openalex.org/W2009303086","https://openalex.org/W2019172585","https://openalex.org/W2059607173","https://openalex.org/W2072931156","https://openalex.org/W2090963365","https://openalex.org/W2100677568","https://openalex.org/W2120465407","https://openalex.org/W2122945138","https://openalex.org/W2139418546","https://openalex.org/W2140778663","https://openalex.org/W2156168464","https://openalex.org/W2156737235","https://openalex.org/W2158091072","https://openalex.org/W2158278868","https://openalex.org/W2173810108","https://openalex.org/W2173945562","https://openalex.org/W2415292238","https://openalex.org/W2545030757","https://openalex.org/W2911283634","https://openalex.org/W2914656440","https://openalex.org/W3041202696","https://openalex.org/W4242606736","https://openalex.org/W4243772471","https://openalex.org/W4285719527","https://openalex.org/W4299512035","https://openalex.org/W4401263623","https://openalex.org/W6635767209"],"related_works":["https://openalex.org/W4255265352","https://openalex.org/W4239477580","https://openalex.org/W4389475841","https://openalex.org/W2952594763","https://openalex.org/W4285537323","https://openalex.org/W2903299703","https://openalex.org/W4385342861","https://openalex.org/W4281791088","https://openalex.org/W2117282672","https://openalex.org/W1574958246"],"abstract_inverted_index":{"We":[0,58,83],"consider":[1],"finite-state":[2],"Markov":[3],"decision":[4],"processes,":[5],"and":[6,9,53,71,94,109,117],"prove":[7,73],"convergence":[8,12,75,88],"rate":[10,89],"of":[11,21,39,43,50,79,90,104],"results":[13],"for":[14,33,76],"certain":[15],"least":[16],"squares":[17],"policy":[18],"evaluation":[19],"algorithms":[20],"the":[22,40,48,66,87,92,95,102],"type":[23],"known":[24,67],"as":[25,123,125],"LSPE(lambda":[26],").":[27],"These":[28],"are":[29,115],"temporal":[30,105],"difference":[31,106],"methods":[32,98,114],"constructing":[34],"a":[35,44,77],"linear":[36],"function":[37,42],"approximation":[38],"cost":[41,55,62,69,97],"stationary":[45],"policy,":[46],"within":[47,101],"context":[49],"infinite-horizon":[51],"discounted":[52,68,93],"average":[54,61,96],"dynamic":[56],"programming.":[57],"introduce":[59],"an":[60],"method,":[63,70],"patterned":[64],"after":[65],"we":[72],"its":[74],"range":[78],"constant":[80],"stepsize":[81],"choices.":[82],"also":[84],"show":[85],"that":[86,112],"both":[91],"is":[99],"optimal":[100],"class":[103],"methods.":[107],"Analysis":[108],"experiment":[110],"indicate":[111],"our":[113],"substantially":[116],"often":[118],"dramatically":[119],"faster":[120],"than":[121],"TD(lambda),":[122],"well":[124],"more":[126],"reliable.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}