{"id":"https://openalex.org/W2114519103","doi":"https://doi.org/10.1109/adprl.2009.4927545","title":"Bounds of optimal learning","display_name":"Bounds of optimal learning","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2114519103","doi":"https://doi.org/10.1109/adprl.2009.4927545","mag":"2114519103"},"language":"en","primary_location":{"id":"doi:10.1109/adprl.2009.4927545","is_oa":false,"landing_page_url":"https://doi.org/10.1109/adprl.2009.4927545","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://eprints.mdx.ac.uk/3489/1/belavkin-bounds_of_optimal_learning.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006396647","display_name":"Roman V. Belavkin","orcid":"https://orcid.org/0000-0002-2356-1447"},"institutions":[{"id":"https://openalex.org/I60488453","display_name":"Middlesex University","ror":"https://ror.org/01rv4p989","country_code":"GB","type":"education","lineage":["https://openalex.org/I60488453"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Roman V. Belavkin","raw_affiliation_strings":["School of Engineering and Information Sciences, Middlesex University, London, UK","(School of Engineering and Information Sciences, Middlesex University, London, UK)"],"affiliations":[{"raw_affiliation_string":"School of Engineering and Information Sciences, Middlesex University, London, UK","institution_ids":["https://openalex.org/I60488453"]},{"raw_affiliation_string":"(School of Engineering and Information Sciences, Middlesex University, London, UK)","institution_ids":["https://openalex.org/I60488453"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006396647"],"corresponding_institution_ids":["https://openalex.org/I60488453"],"apc_list":null,"apc_paid":null,"fwci":1.8065,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.87830497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","issue":null,"first_page":"199","last_page":"204"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9919000267982483,"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/T10320","display_name":"Neural Networks and Applications","score":0.9919000267982483,"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/T11236","display_name":"Control Systems and Identification","score":0.9758999943733215,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9753999710083008,"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/trajectory","display_name":"Trajectory","score":0.6000121235847473},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5873584151268005},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5759490728378296},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.5716762542724609},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5516588687896729},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5002110004425049},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.4970386326313019},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4935206174850464},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4742373824119568},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4569450318813324},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4458431303501129},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4416015148162842},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.42913779616355896},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42711085081100464},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.4181060791015625},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41062864661216736},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20257455110549927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16517487168312073},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10109707713127136}],"concepts":[{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6000121235847473},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5873584151268005},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5759490728378296},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.5716762542724609},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5516588687896729},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5002110004425049},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.4970386326313019},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4935206174850464},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4742373824119568},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4569450318813324},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4458431303501129},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4416015148162842},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.42913779616355896},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42711085081100464},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.4181060791015625},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41062864661216736},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20257455110549927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16517487168312073},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10109707713127136},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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":3,"locations":[{"id":"doi:10.1109/adprl.2009.4927545","is_oa":false,"landing_page_url":"https://doi.org/10.1109/adprl.2009.4927545","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning","raw_type":"proceedings-article"},{"id":"pmh:oai:eprints.mdx.ac.uk:3489","is_oa":true,"landing_page_url":null,"pdf_url":"https://eprints.mdx.ac.uk/3489/1/belavkin-bounds_of_optimal_learning.pdf","source":{"id":"https://openalex.org/S4306400025","display_name":"Middlesex University Research Repository (Middlesex University Of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60488453","host_organization_name":"Middlesex University","host_organization_lineage":["https://openalex.org/I60488453"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.950.4231","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.950.4231","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.mdx.ac.uk/3489/1/belavkin-bounds_of_optimal_learning.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:eprints.mdx.ac.uk:3489","is_oa":true,"landing_page_url":null,"pdf_url":"https://eprints.mdx.ac.uk/3489/1/belavkin-bounds_of_optimal_learning.pdf","source":{"id":"https://openalex.org/S4306400025","display_name":"Middlesex University Research Repository (Middlesex University Of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60488453","host_organization_name":"Middlesex University","host_organization_lineage":["https://openalex.org/I60488453"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2114519103.pdf","grobid_xml":"https://content.openalex.org/works/W2114519103.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W107085514","https://openalex.org/W176248852","https://openalex.org/W646945617","https://openalex.org/W1489222793","https://openalex.org/W1577338488","https://openalex.org/W1587799944","https://openalex.org/W1989892763","https://openalex.org/W1995875735","https://openalex.org/W2032558547","https://openalex.org/W2034541289","https://openalex.org/W2036422857","https://openalex.org/W2043299091","https://openalex.org/W2046495522","https://openalex.org/W2107726111","https://openalex.org/W2112088249","https://openalex.org/W2112863458","https://openalex.org/W2121863487","https://openalex.org/W2123838014","https://openalex.org/W2138789208","https://openalex.org/W2310516540","https://openalex.org/W2334591577","https://openalex.org/W2341171179","https://openalex.org/W3206777520","https://openalex.org/W4214717370","https://openalex.org/W6629257553","https://openalex.org/W6676919016","https://openalex.org/W6680677096"],"related_works":["https://openalex.org/W1742234374","https://openalex.org/W334503494","https://openalex.org/W2155379735","https://openalex.org/W23557442","https://openalex.org/W4291625303","https://openalex.org/W4387297266","https://openalex.org/W4213369954","https://openalex.org/W2805484063","https://openalex.org/W2737579912","https://openalex.org/W2326043905"],"abstract_inverted_index":{"Learning":[0],"is":[1,18],"considered":[2],"as":[3],"a":[4,9,12,16,94],"dynamic":[5],"process":[6],"described":[7],"by":[8],"trajectory":[10],"on":[11],"statistical":[13,106],"manifold,":[14],"and":[15,61,90,108],"topology":[17],"introduced":[19],"defining":[20,87],"trajectories":[21,72],"continuous":[22],"in":[23,33,49,111,125],"information.":[24],"The":[25],"analysis":[26],"generalises":[27],"the":[28,85,122],"application":[29],"of":[30,51,69,93,105,121],"Orlicz":[31],"spaces":[32,40,47],"non-parametric":[34],"information":[35,91,112],"geometry":[36],"to":[37],"topological":[38],"function":[39],"with":[41],"asymmetric":[42],"gauge":[43],"functions":[44],"(e.g.":[45],"quasi-metric":[46],"defined":[48],"terms":[50],"KL":[52],"divergence).":[53],"Optimality":[54],"conditions":[55],"are":[56,65],"formulated":[57],"for":[58,84,119],"dynamical":[59],"constraints,":[60],"two":[62],"main":[63],"results":[64,98],"outlined:":[66],"1)":[67],"Parametrisation":[68],"optimal":[70,88],"learning":[71,95,127],"from":[73],"empirical":[74],"constraints":[75],"using":[76],"generalised":[77],"characteristic":[78],"potentials;":[79],"2)":[80],"A":[81],"gradient":[82],"theorem":[83],"potentials":[86],"utility":[89],"bounds":[92],"system.":[96],"These":[97],"not":[99],"only":[100],"generalise":[101],"some":[102],"known":[103],"relations":[104],"mechanics":[107],"variational":[109],"methods":[110],"theory,":[113],"but":[114],"also":[115],"can":[116],"be":[117],"used":[118],"optimisation":[120],"exploration-exploitation":[123],"balance":[124],"online":[126],"systems.":[128]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}