{"id":"https://openalex.org/W2124856311","doi":"https://doi.org/10.1109/tac.2012.2186176","title":"Mean Field for Markov Decision Processes: From Discrete to Continuous Optimization","display_name":"Mean Field for Markov Decision Processes: From Discrete to Continuous Optimization","publication_year":2012,"publication_date":"2012-02-01","ids":{"openalex":"https://openalex.org/W2124856311","doi":"https://doi.org/10.1109/tac.2012.2186176","mag":"2124856311"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2012.2186176","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2186176","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1004.2342","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052639125","display_name":"Nicolas Gast","orcid":"https://orcid.org/0000-0001-6884-8698"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"id":"https://openalex.org/I97565354","display_name":"University of Lausanne","ror":"https://ror.org/019whta54","country_code":"CH","type":"education","lineage":["https://openalex.org/I97565354"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Nicolas Gast","raw_affiliation_strings":["IC-LCA2, EPF Lausanne, Lausanne, Switzerland","LCA2, EPFL, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"IC-LCA2, EPF Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864","https://openalex.org/I97565354"]},{"raw_affiliation_string":"LCA2, EPFL, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073088518","display_name":"Bruno Gaujal","orcid":"https://orcid.org/0000-0001-9081-8401"},"institutions":[{"id":"https://openalex.org/I4210104430","display_name":"Laboratoire d'Informatique de Grenoble","ror":"https://ror.org/01c8rcg82","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I4210101348","display_name":"Centre Inria de l'Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/00n8d6z93","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210101348"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bruno Gaujal","raw_affiliation_strings":["LIG, INRIA Grenoble Rh\u00f4ne-Alpes, Montbonnot, France","LIG, INRIA Grenoble-Rhone-Alpes, Montbonnot, France"],"affiliations":[{"raw_affiliation_string":"LIG, INRIA Grenoble Rh\u00f4ne-Alpes, Montbonnot, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210101348","https://openalex.org/I4210104430"]},{"raw_affiliation_string":"LIG, INRIA Grenoble-Rhone-Alpes, Montbonnot, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210104430"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113673271","display_name":"Jean-Yves Le Boudec","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"id":"https://openalex.org/I97565354","display_name":"University of Lausanne","ror":"https://ror.org/019whta54","country_code":"CH","type":"education","lineage":["https://openalex.org/I97565354"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Jean-Yves Le Boudec","raw_affiliation_strings":["IC-LCA2, EPF Lausanne, Lausanne, Switzerland","LCA2, EPFL, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"IC-LCA2, EPF Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864","https://openalex.org/I97565354"]},{"raw_affiliation_string":"LCA2, EPFL, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052639125"],"corresponding_institution_ids":["https://openalex.org/I5124864","https://openalex.org/I97565354"],"apc_list":null,"apc_paid":null,"fwci":18.8424,"has_fulltext":false,"cited_by_count":100,"citation_normalized_percentile":{"value":0.9945067,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"57","issue":"9","first_page":"2266","last_page":"2280"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11195","display_name":"Simulation Techniques and Applications","score":0.9908999800682068,"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"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.9227784872055054},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.661601185798645},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.6591559648513794},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6225913166999817},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.6091402769088745},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5550099015235901},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5308678150177002},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5186356902122498},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.4683881103992462},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.44250428676605225},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.42036187648773193},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.4164086580276489},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.41302162408828735},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.30863288044929504},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21070224046707153}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.9227784872055054},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.661601185798645},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.6591559648513794},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6225913166999817},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.6091402769088745},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5550099015235901},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5308678150177002},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5186356902122498},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.4683881103992462},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.44250428676605225},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.42036187648773193},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.4164086580276489},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.41302162408828735},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.30863288044929504},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21070224046707153},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tac.2012.2186176","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2186176","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:arXiv.org:1004.2342","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1004.2342","pdf_url":"https://arxiv.org/pdf/1004.2342","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":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.173.8964","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.173.8964","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://infoscience.epfl.ch/record/148261/files/optimal_mf_convergence.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00787996v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-00787996","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2012, 57 (9), pp.2266 - 2280. &#x27E8;10.1109/TAC.2012.2186176&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:infoscience.epfl.ch:174758","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/174758","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"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":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1004.2342","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1004.2342","pdf_url":"https://arxiv.org/pdf/1004.2342","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W202681721","https://openalex.org/W565357261","https://openalex.org/W1491706803","https://openalex.org/W1568229137","https://openalex.org/W1568863439","https://openalex.org/W1745373831","https://openalex.org/W1972673017","https://openalex.org/W1983321045","https://openalex.org/W1984697146","https://openalex.org/W1992326878","https://openalex.org/W2011000015","https://openalex.org/W2016448831","https://openalex.org/W2024303441","https://openalex.org/W2029804570","https://openalex.org/W2033593383","https://openalex.org/W2038686546","https://openalex.org/W2042592362","https://openalex.org/W2062259223","https://openalex.org/W2079969476","https://openalex.org/W2088346346","https://openalex.org/W2100594181","https://openalex.org/W2105518356","https://openalex.org/W2105556121","https://openalex.org/W2117966169","https://openalex.org/W2119567691","https://openalex.org/W2123807026","https://openalex.org/W2131056547","https://openalex.org/W2132511141","https://openalex.org/W2139418546","https://openalex.org/W2148301044","https://openalex.org/W2161728228","https://openalex.org/W2334782222","https://openalex.org/W2529850387","https://openalex.org/W2799087070","https://openalex.org/W2959560348","https://openalex.org/W3124066568","https://openalex.org/W4229487429"],"related_works":["https://openalex.org/W4239477580","https://openalex.org/W4255265352","https://openalex.org/W2921905705","https://openalex.org/W1632524629","https://openalex.org/W4292330635","https://openalex.org/W2902017027","https://openalex.org/W2766998270","https://openalex.org/W2950982235","https://openalex.org/W4306892756","https://openalex.org/W2052286527"],"abstract_inverted_index":{"We":[0,22,60,89],"study":[1],"the":[2,25,41,51,56,64,67,78,86,91,115,118,124],"convergence":[3],"of":[4,9,13,28,43,55,66,85,117,126],"Markov":[5,31,57,79],"decision":[6,32,58,80],"processes,":[7],"composed":[8],"a":[10,30,36,44,83,128,134],"large":[11,135],"number":[12],"objects,":[14],"to":[15,40,77,98,111,122],"optimization":[16],"problems":[17],"on":[18,50,63,93],"ordinary":[19],"differential":[20],"equations.":[21,88],"show":[23,123],"that":[24],"optimal":[26],"reward":[27],"such":[29],"process,":[33],"which":[34],"satisfies":[35],"Bellman":[37,137],"equation,":[38],"converges":[39],"solution":[42,76,84],"continuous":[45,129],"Hamilton-Jacobi-Bellman":[46],"(HJB)":[47],"equation":[48,131],"based":[49],"mean":[52],"field":[53],"approximation":[54],"process.":[59],"give":[61],"bounds":[62],"difference":[65],"rewards":[68],"and":[69,104,113,121],"an":[70,74],"algorithm":[71],"for":[72],"deriving":[73],"approximating":[75],"process":[81],"from":[82],"HJB":[87,130],"illustrate":[90,112],"method":[92],"three":[94],"examples":[95],"pertaining,":[96],"respectively,":[97],"investment":[99],"strategies,":[100],"population":[101],"dynamics":[102],"control":[103],"scheduling":[105],"in":[106],"queues.":[107],"They":[108],"are":[109],"used":[110],"justify":[114],"construction":[116],"controlled":[119],"ODE":[120],"advantage":[125],"solving":[127],"rather":[132],"than":[133],"discrete":[136],"equation.":[138]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":9}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
