{"id":"https://openalex.org/W2070844704","doi":"https://doi.org/10.1109/adprl.2011.5967383","title":"Moving least-squares approximations for linearly-solvable MDP","display_name":"Moving least-squares approximations for linearly-solvable MDP","publication_year":2011,"publication_date":"2011-04-01","ids":{"openalex":"https://openalex.org/W2070844704","doi":"https://doi.org/10.1109/adprl.2011.5967383","mag":"2070844704"},"language":"en","primary_location":{"id":"doi:10.1109/adprl.2011.5967383","is_oa":false,"landing_page_url":"https://doi.org/10.1109/adprl.2011.5967383","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5016365745","display_name":"Mingyuan Zhong","orcid":"https://orcid.org/0000-0003-3184-759X"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]},{"id":"https://openalex.org/I58610484","display_name":"Seattle University","ror":"https://ror.org/02jqc0m91","country_code":"US","type":"education","lineage":["https://openalex.org/I58610484"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mingyuan Zhong","raw_affiliation_strings":["Department of Applied Mathematics, University of Washington, Seattle, WA, USA","Department of Applied Mathematics, University of Washington, Seattle, 98195, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I4210138199"]},{"raw_affiliation_string":"Department of Applied Mathematics, University of Washington, Seattle, 98195, USA","institution_ids":["https://openalex.org/I201448701","https://openalex.org/I4210138199","https://openalex.org/I58610484"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108520754","display_name":"Emanuel Todorov","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Emanuel Todorov","raw_affiliation_strings":["Department of Applied Mathematics Department of Computer Science and Engineering, University of Washington, Seattle, WA, USA","Department of Applied Mathematics, Department of Computer Science and Engineering, University of Washington, Seattle, 98195, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics Department of Computer Science and Engineering, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"Department of Applied Mathematics, Department of Computer Science and Engineering, University of Washington, Seattle, 98195, USA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.20360025,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"26","issue":null,"first_page":"218","last_page":"225"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9750000238418579,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9733999967575073,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6717866659164429},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5699583292007446},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.5107407569885254},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4955350160598755},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49286961555480957},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4793732464313507},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4752756655216217},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4697813093662262},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4477366507053375},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.44730043411254883},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43964701890945435},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4262021780014038},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41506925225257874},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39037325978279114},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.37184494733810425},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10033124685287476}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6717866659164429},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5699583292007446},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.5107407569885254},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4955350160598755},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49286961555480957},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4793732464313507},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4752756655216217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4697813093662262},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4477366507053375},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.44730043411254883},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43964701890945435},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4262021780014038},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41506925225257874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39037325978279114},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.37184494733810425},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10033124685287476},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/adprl.2011.5967383","is_oa":false,"landing_page_url":"https://doi.org/10.1109/adprl.2011.5967383","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7699999809265137,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"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":9,"referenced_works":["https://openalex.org/W1576347883","https://openalex.org/W2043962331","https://openalex.org/W2072273591","https://openalex.org/W2093524643","https://openalex.org/W2101121254","https://openalex.org/W2128152413","https://openalex.org/W2145060720","https://openalex.org/W4320800818","https://openalex.org/W6681439324"],"related_works":["https://openalex.org/W2370840338","https://openalex.org/W2388641108","https://openalex.org/W4296209631","https://openalex.org/W2368317224","https://openalex.org/W2807018115","https://openalex.org/W4200250224","https://openalex.org/W2285658092","https://openalex.org/W4388236136","https://openalex.org/W2126560268","https://openalex.org/W1996326480"],"abstract_inverted_index":{"By":[0],"introducing":[1],"Linearly-solvable":[2],"Markov":[3],"Decision":[4],"Process":[5],"(LMDP),":[6],"a":[7,45,54,123,134],"general":[8],"class":[9],"of":[10,38,75,90,102,112,137],"nonlinear":[11],"stochastic":[12],"optimal":[13],"control":[14],"problems":[15,143,153],"can":[16],"be":[17],"reduced":[18],"to":[19,35,95,152],"solving":[20],"linear":[21],"problems.":[22],"However,":[23],"in":[24,122,128],"practice,":[25],"LMDP":[26],"defined":[27,117],"on":[28,83,141],"continuous":[29],"state":[30,40,103],"space":[31,104],"remain":[32],"difficult":[33],"due":[34],"high":[36,155],"dimensionality":[37],"the":[39,91,100,113,119,129],"space.":[41],"Here":[42],"we":[43,70],"describe":[44],"new":[46],"framework":[47],"for":[48],"finding":[49],"this":[50],"solution":[51],"by":[52],"using":[53],"moving":[55],"least-squares":[56],"approximation.":[57],"We":[58],"use":[59],"efficient":[60],"iterative":[61],"solvers":[62],"which":[63,86],"do":[64],"not":[65],"require":[66],"matrix":[67],"factorization,":[68],"so":[69,93],"could":[71],"handle":[72],"large":[73],"numbers":[74],"bases.":[76],"The":[77,110],"basis":[78],"functions":[79],"are":[80,106,144],"constructed":[81],"based":[82],"collocation":[84,120],"states":[85],"change":[87],"over":[88],"iterations":[89],"algorithm,":[92],"as":[94],"provide":[96],"higher":[97],"resolution":[98],"at":[99],"regions":[101],"that":[105,125],"visited":[107],"more":[108],"often.":[109],"shape":[111],"bases":[114],"is":[115],"automatically":[116],"given":[118],"states,":[121],"way":[124],"avoids":[126,132],"gaps":[127],"coverage":[130],"and":[131,146],"fitting":[133],"tremendous":[135],"amount":[136],"parameters.":[138],"Numerical":[139],"results":[140],"test":[142],"provided":[145],"demonstrate":[147],"good":[148],"behavior":[149],"when":[150],"scaled":[151],"with":[154],"dimensionality.":[156]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
