{"id":"https://openalex.org/W2116459397","doi":"https://doi.org/10.1145/1143844.1143932","title":"An analytic solution to discrete Bayesian reinforcement learning","display_name":"An analytic solution to discrete Bayesian reinforcement learning","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2116459397","doi":"https://doi.org/10.1145/1143844.1143932","mag":"2116459397"},"language":"en","primary_location":{"id":"doi:10.1145/1143844.1143932","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1143844.1143932","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 23rd international conference on Machine learning  - ICML '06","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://orbilu.uni.lu/handle/10993/11055","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050467922","display_name":"Pascal Poupart","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pascal Poupart","raw_affiliation_strings":["University of Waterloo, Waterloo, Ontario, Canada","University of Waterloo, Waterloo, Ontario, CANADA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of Waterloo, Waterloo, Ontario, CANADA","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082325811","display_name":"Nikos Vlassis","orcid":null},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Nikos Vlassis","raw_affiliation_strings":["University of Amsterdam, Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Amsterdam, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071941660","display_name":"Jesse Hoey","orcid":"https://orcid.org/0000-0001-5340-2204"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jesse Hoey","raw_affiliation_strings":["University of Toronto, Toronto, Ontario, Canada","* University of Toronto, Toronto, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, Ontario, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"* University of Toronto, Toronto, Ontario, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078411059","display_name":"Kevin Regan","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Kevin Regan","raw_affiliation_strings":["University of Waterloo, Waterloo, Ontario, Canada","University of Waterloo, Waterloo, Ontario, CANADA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of Waterloo, Waterloo, Ontario, CANADA","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":296,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"697","last_page":"704"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9943000078201294,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9943000078201294,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.993399977684021,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/reinforcement-learning","display_name":"Reinforcement learning","score":0.8344098925590515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7475842833518982},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.7436076998710632},{"id":"https://openalex.org/keywords/exploit","display_name":"Exploit","score":0.581313967704773},{"id":"https://openalex.org/keywords/partially-observable-markov-decision-process","display_name":"Partially observable Markov decision process","score":0.5471332669258118},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5367404818534851},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5279254913330078},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4716557562351227},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.44407713413238525},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.4434754550457001},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4251860976219177},{"id":"https://openalex.org/keywords/online-learning","display_name":"Online learning","score":0.41539275646209717},{"id":"https://openalex.org/keywords/online-algorithm","display_name":"Online algorithm","score":0.41353198885917664},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.36032944917678833},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.3226262331008911},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32098841667175293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16998502612113953},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.16860589385032654}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.8344098925590515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7475842833518982},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.7436076998710632},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.581313967704773},{"id":"https://openalex.org/C17098449","wikidata":"https://www.wikidata.org/wiki/Q176814","display_name":"Partially observable Markov decision process","level":4,"score":0.5471332669258118},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5367404818534851},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5279254913330078},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4716557562351227},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.44407713413238525},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4434754550457001},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4251860976219177},{"id":"https://openalex.org/C2986087404","wikidata":"https://www.wikidata.org/wiki/Q15946010","display_name":"Online learning","level":2,"score":0.41539275646209717},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.41353198885917664},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.36032944917678833},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3226262331008911},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32098841667175293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16998502612113953},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.16860589385032654},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","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},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1145/1143844.1143932","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1143844.1143932","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 23rd international conference on Machine learning  - ICML '06","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.126.1774","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.126.1774","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uwaterloo.ca/~kmregan/files/icml-brl-9pages.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.226.8223","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.226.8223","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/%7Ekmregan/files/icml06.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.68.470","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.68.470","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uwaterloo.ca/~ppoupart/publications/bayesian-rl/icml-brl-8pages.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.68.6229","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.68.6229","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uwaterloo.ca/~ppoupart/publications/bayesian-rl/icml-brl-8pages.pdf","raw_type":"text"},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/fad96ca9-3ca8-4326-abe6-ecdfdd866dbc","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/an-analytic-solution-to-discrete-bayesian-reinforcement-learning(fad96ca9-3ca8-4326-abe6-ecdfdd866dbc).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Poupart, P, Vlassis, N, Hoey, J & Regan, K 2006, An analytic solution to discrete Bayesian reinforcement learning. in Proc. Int. Conf. on Machine Learning. Pittsburgh, USA, pp. 697-704.","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:dare.uva.nl:publications/fad96ca9-3ca8-4326-abe6-ecdfdd866dbc","is_oa":false,"landing_page_url":"http://dare.uva.nl/personal/pure/en/publications/an-analytic-solution-to-discrete-bayesian-reinforcement-learning(fad96ca9-3ca8-4326-abe6-ecdfdd866dbc).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Poupart, P, Vlassis, N, Hoey, J & Regan, K 2006, An analytic solution to discrete Bayesian reinforcement learning. in Proc. Int. Conf. on Machine Learning. Pittsburgh, USA, pp. 697-704.","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:orbilu.uni.lu:10993/11055","is_oa":true,"landing_page_url":"http://orbilu.uni.lu/handle/10993/11055","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proc Int. Conf. on Machine Learning, Pittsburgh, USA, 697-704 (2006); Int. Conf. on Machine Learning, Pittsburgh, USA, 2006","raw_type":"http://purl.org/coar/resource_type/c_5794"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/fad96ca9-3ca8-4326-abe6-ecdfdd866dbc","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/an-analytic-solution-to-discrete-bayesian-reinforcement-learning(fad96ca9-3ca8-4326-abe6-ecdfdd866dbc).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proc. Int. Conf. on Machine Learning, 697 - 704","raw_type":"info:eu-repo/semantics/conferencepaper"}],"best_oa_location":{"id":"pmh:oai:orbilu.uni.lu:10993/11055","is_oa":true,"landing_page_url":"http://orbilu.uni.lu/handle/10993/11055","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proc Int. Conf. on Machine Learning, Pittsburgh, USA, 697-704 (2006); Int. Conf. on Machine Learning, Pittsburgh, USA, 2006","raw_type":"http://purl.org/coar/resource_type/c_5794"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6499999761581421}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W36013382","https://openalex.org/W1496855202","https://openalex.org/W1497039698","https://openalex.org/W1515933446","https://openalex.org/W1582436621","https://openalex.org/W1591803298","https://openalex.org/W1931792391","https://openalex.org/W1949804828","https://openalex.org/W2006258746","https://openalex.org/W2034725503","https://openalex.org/W2071814471","https://openalex.org/W2108734173","https://openalex.org/W2117341272","https://openalex.org/W2128775537","https://openalex.org/W2296381616","https://openalex.org/W2470235696","https://openalex.org/W2787259794","https://openalex.org/W2911283634","https://openalex.org/W2914656440","https://openalex.org/W3101822862"],"related_works":["https://openalex.org/W2096013579","https://openalex.org/W52153049","https://openalex.org/W1760611253","https://openalex.org/W1515117609","https://openalex.org/W1589140671","https://openalex.org/W4323315247","https://openalex.org/W2294884454","https://openalex.org/W3169161914","https://openalex.org/W4321379664","https://openalex.org/W2211790881"],"abstract_inverted_index":{"Reinforcement":[0],"learning":[1,59,73],"(RL)":[2],"was":[3],"originally":[4],"proposed":[5],"as":[6,18,92],"a":[7,51,65,86,93,117],"framework":[8],"to":[9,12],"allow":[10],"agents":[11],"learn":[13],"in":[14,60],"an":[15,123],"online":[16,48,72],"fashion":[17],"they":[19],"interact":[20],"with":[21],"their":[22],"environment.":[23],"Existing":[24],"RL":[25,53,91],"algorithms":[26],"come":[27],"short":[28],"of":[29,36,82,116,119],"achieving":[30],"this":[31,131],"goal":[32],"because":[33],"the":[34,80,104,108,113],"amount":[35,81],"exploration":[37],"required":[38],"is":[39,54,75,112],"often":[40],"too":[41,44],"costly":[42],"and/or":[43],"time":[45],"consuming":[46],"for":[47,57,70],"learning.":[49],"As":[50],"result,":[52],"mostly":[55],"used":[56],"offline":[58],"simulated":[61],"environments.":[62],"We":[63,84],"propose":[64],"new":[66],"algorithm,":[67],"called":[68],"BEETLE,":[69],"effective":[71],"that":[74,107,129],"computationally":[76],"efficient":[77,124],"while":[78],"minimizing":[79],"exploration.":[83],"take":[85],"Bayesian":[87],"model-based":[88],"approach,":[89],"framing":[90],"partially":[94],"observable":[95],"Markov":[96],"decision":[97],"process.":[98],"Our":[99],"two":[100],"main":[101],"contributions":[102],"are":[103],"analytical":[105],"derivation":[106],"optimal":[109],"value":[110,126],"function":[111],"upper":[114],"envelope":[115],"set":[118],"multivariate":[120],"polynomials,":[121],"and":[122],"point-based":[125],"iteration":[127],"algorithm":[128],"exploits":[130],"simple":[132],"parameterization.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":31},{"year":2012,"cited_by_count":38}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}