{"id":"https://openalex.org/W2141022000","doi":"https://doi.org/10.1137/100807879","title":"Least Squares Temporal Difference Methods: An Analysis under General Conditions","display_name":"Least Squares Temporal Difference Methods: An Analysis under General Conditions","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2141022000","doi":"https://doi.org/10.1137/100807879","mag":"2141022000"},"language":"en","primary_location":{"id":"doi:10.1137/100807879","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100807879","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/1721.1/77629","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/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"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":["US"],"is_corresponding":true,"raw_author_name":"Huizhen Yu","raw_affiliation_strings":["Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014937312"],"corresponding_institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":4.4199,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.94534988,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"6","first_page":"3310","last_page":"3343"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9991000294685364,"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":0.9991000294685364,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9929999709129333,"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":0.9907000064849854,"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/mathematics","display_name":"Mathematics","score":0.8252487778663635},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.719753086566925},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7028526067733765},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5982195734977722},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5624834895133972},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5290176868438721},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4896307587623596},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46702030301094055},{"id":"https://openalex.org/keywords/markov-kernel","display_name":"Markov kernel","score":0.465999960899353},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.44815337657928467},{"id":"https://openalex.org/keywords/finite-state","display_name":"Finite state","score":0.4366987645626068},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4335736632347107},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.41389769315719604},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.41312357783317566},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37442854046821594},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.3329334259033203},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.33092525601387024},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2306612730026245},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.22704529762268066},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1480751931667328},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10261201858520508},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09879794716835022}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8252487778663635},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.719753086566925},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7028526067733765},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5982195734977722},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5624834895133972},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5290176868438721},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4896307587623596},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46702030301094055},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.465999960899353},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.44815337657928467},{"id":"https://openalex.org/C2983497884","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite state","level":3,"score":0.4366987645626068},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4335736632347107},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.41389769315719604},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.41312357783317566},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37442854046821594},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.3329334259033203},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.33092525601387024},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2306612730026245},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.22704529762268066},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1480751931667328},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10261201858520508},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09879794716835022},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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":3,"locations":[{"id":"doi:10.1137/100807879","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100807879","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/77629","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/77629","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":"SIAM","raw_type":"http://purl.org/eprint/type/JournalArticle"},{"id":"pmh:oai:helda.helsinki.fi:10138/17799","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/17799","pdf_url":null,"source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Tekninen raportti"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/77629","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/77629","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":"SIAM","raw_type":"http://purl.org/eprint/type/JournalArticle"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6000000238418579,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320337253","display_name":"Instituto de Ciencias del Mar y Limnolog\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W565357261","https://openalex.org/W985816301","https://openalex.org/W1499021337","https://openalex.org/W1507222174","https://openalex.org/W1529558080","https://openalex.org/W1576452626","https://openalex.org/W1594216983","https://openalex.org/W1594563152","https://openalex.org/W1597303641","https://openalex.org/W1600046456","https://openalex.org/W1995713768","https://openalex.org/W1997394097","https://openalex.org/W2002142848","https://openalex.org/W2019172585","https://openalex.org/W2027648864","https://openalex.org/W2072931156","https://openalex.org/W2073733021","https://openalex.org/W2075268401","https://openalex.org/W2087018957","https://openalex.org/W2098432798","https://openalex.org/W2100677568","https://openalex.org/W2104753538","https://openalex.org/W2108596215","https://openalex.org/W2119567691","https://openalex.org/W2121825831","https://openalex.org/W2124144580","https://openalex.org/W2129935817","https://openalex.org/W2130599357","https://openalex.org/W2139418546","https://openalex.org/W2140778663","https://openalex.org/W2154761920","https://openalex.org/W2158126207","https://openalex.org/W2799137445","https://openalex.org/W2911283634","https://openalex.org/W2914656440","https://openalex.org/W3150304496"],"related_works":["https://openalex.org/W1050019105","https://openalex.org/W2107384771","https://openalex.org/W2014747857","https://openalex.org/W1598942703","https://openalex.org/W2102962763","https://openalex.org/W2130519334","https://openalex.org/W2016588739","https://openalex.org/W1595080983","https://openalex.org/W2808750934","https://openalex.org/W2021298813"],"abstract_inverted_index":{"We":[0,49,65],"consider":[1],"approximate":[2],"policy":[3,29,46],"evaluation":[4],"for":[5,51],"finite":[6,90],"state":[7,133],"and":[8,81,94,113,127,134],"action":[9,135],"Markov":[10,37,92,97],"decision":[11],"processes":[12],"(MDP)":[13],"with":[14,131,148],"the":[15,41,45,52,71,75],"least":[16],"squares":[17],"temporal":[18,110],"difference":[19,111],"(LSTD)":[20],"algorithm,":[21,76],"LSTD($\\lambda$),":[22],"in":[23,74,79],"an":[24],"exploration-enhanced":[25],"learning":[26],"context,":[27],"where":[28],"costs":[30],"are":[31],"computed":[32],"from":[33,40],"observations":[34],"of":[35,70,88,123,143],"a":[36,100,120,124,140,144],"chain":[38],"different":[39],"one":[42],"corresponding":[43],"to":[44,108,129],"under":[47,61],"evaluation.":[48],"establish":[50],"discounted":[53],"cost":[54],"criterion":[55],"that":[56],"LSTD($\\lambda$)":[57],"converges":[58],"almost":[59],"surely":[60],"mild,":[62],"minimal":[63],"conditions.":[64],"also":[66],"analyze":[67],"other":[68,109],"properties":[69],"iterates":[72],"involved":[73],"including":[77],"convergence":[78,121,141],"mean":[80],"boundedness.":[82],"Our":[83,103],"analysis":[84,122],"draws":[85],"on":[86,99],"theories":[87],"both":[89],"space":[91],"chains":[93,98],"weak":[95],"Feller":[96],"topological":[101],"space.":[102],"results":[104],"can":[105],"be":[106],"applied":[107],"algorithms":[112],"MDP":[114,130],"models.":[115],"As":[116],"examples,":[117],"we":[118],"give":[119],"TD($\\lambda$)":[125],"algorithm":[126,147],"extensions":[128],"compact":[132],"spaces,":[136],"as":[137,139],"well":[138],"proof":[142],"new":[145],"LSTD":[146],"state-dependent":[149],"$\\lambda$-parameters.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}