{"id":"https://openalex.org/W4414487421","doi":"https://doi.org/10.3389/frobt.2025.1649154","title":"Weber\u2013Fechner law in temporal difference learning derived from control as inference","display_name":"Weber\u2013Fechner law in temporal difference learning derived from control as inference","publication_year":2025,"publication_date":"2025-09-25","ids":{"openalex":"https://openalex.org/W4414487421","doi":"https://doi.org/10.3389/frobt.2025.1649154","pmid":"https://pubmed.ncbi.nlm.nih.gov/41080713"},"language":"en","primary_location":{"id":"doi:10.3389/frobt.2025.1649154","is_oa":true,"landing_page_url":"https://doi.org/10.3389/frobt.2025.1649154","pdf_url":"https://www.frontiersin.org/journals/robotics-and-ai/articles/10.3389/frobt.2025.1649154/pdf","source":{"id":"https://openalex.org/S2595095599","display_name":"Frontiers in Robotics and AI","issn_l":"2296-9144","issn":["2296-9144"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Robotics and AI","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/journals/robotics-and-ai/articles/10.3389/frobt.2025.1649154/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046583369","display_name":"Kei Takahashi","orcid":"https://orcid.org/0000-0001-5996-8532"},"institutions":[{"id":"https://openalex.org/I75917431","display_name":"Nara Institute of Science and Technology","ror":"https://ror.org/05bhada84","country_code":"JP","type":"education","lineage":["https://openalex.org/I75917431"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Keiichiro Takahashi","raw_affiliation_strings":["Division of Information Science, Nara Institute of Science and Technology, Ikoma, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Information Science, Nara Institute of Science and Technology, Ikoma, Japan","institution_ids":["https://openalex.org/I75917431"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051304187","display_name":"Taisuke Kobayashi","orcid":"https://orcid.org/0000-0002-3760-249X"},"institutions":[{"id":"https://openalex.org/I184597095","display_name":"National Institute of Informatics","ror":"https://ror.org/04ksd4g47","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I184597095","https://openalex.org/I4210158934"]},{"id":"https://openalex.org/I200475212","display_name":"The Graduate University for Advanced Studies, SOKENDAI","ror":"https://ror.org/0516ah480","country_code":"JP","type":"education","lineage":["https://openalex.org/I200475212"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Taisuke Kobayashi","raw_affiliation_strings":["National Institute of Informatics (NII) and The Graduate University for Advanced Studies (SOKENDAI), Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institute of Informatics (NII) and The Graduate University for Advanced Studies (SOKENDAI), Tokyo, Japan","institution_ids":["https://openalex.org/I200475212","https://openalex.org/I184597095"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003009172","display_name":"Tomoya Yamanokuchi","orcid":"https://orcid.org/0000-0003-2387-2197"},"institutions":[{"id":"https://openalex.org/I75917431","display_name":"Nara Institute of Science and Technology","ror":"https://ror.org/05bhada84","country_code":"JP","type":"education","lineage":["https://openalex.org/I75917431"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tomoya Yamanokuchi","raw_affiliation_strings":["Division of Information Science, Nara Institute of Science and Technology, Ikoma, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Information Science, Nara Institute of Science and Technology, Ikoma, Japan","institution_ids":["https://openalex.org/I75917431"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042074952","display_name":"Takamitsu Matsubara","orcid":"https://orcid.org/0000-0003-3545-4814"},"institutions":[{"id":"https://openalex.org/I75917431","display_name":"Nara Institute of Science and Technology","ror":"https://ror.org/05bhada84","country_code":"JP","type":"education","lineage":["https://openalex.org/I75917431"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takamitsu Matsubara","raw_affiliation_strings":["Division of Information Science, Nara Institute of Science and Technology, Ikoma, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Information Science, Nara Institute of Science and Technology, Ikoma, Japan","institution_ids":["https://openalex.org/I75917431"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5051304187"],"corresponding_institution_ids":["https://openalex.org/I184597095","https://openalex.org/I200475212"],"apc_list":{"value":1900,"currency":"USD","value_usd":1900},"apc_paid":{"value":1900,"currency":"USD","value_usd":1900},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12574048,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":null,"first_page":"1649154","last_page":"1649154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9934999942779541,"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":0.9934999942779541,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9869999885559082,"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/reinforcement-learning","display_name":"Reinforcement learning","score":0.7581999897956848},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6552000045776367},{"id":"https://openalex.org/keywords/temporal-difference-learning","display_name":"Temporal difference learning","score":0.6014999747276306},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.5942999720573425},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5418999791145325},{"id":"https://openalex.org/keywords/perception","display_name":"Perception","score":0.48739999532699585},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.43860000371932983},{"id":"https://openalex.org/keywords/q-learning","display_name":"Q-learning","score":0.421999990940094}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.7581999897956848},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7128000259399414},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6552000045776367},{"id":"https://openalex.org/C196340769","wikidata":"https://www.wikidata.org/wiki/Q7698910","display_name":"Temporal difference learning","level":3,"score":0.6014999747276306},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.5942999720573425},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5418999791145325},{"id":"https://openalex.org/C26760741","wikidata":"https://www.wikidata.org/wiki/Q160402","display_name":"Perception","level":2,"score":0.48739999532699585},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.43860000371932983},{"id":"https://openalex.org/C188116033","wikidata":"https://www.wikidata.org/wiki/Q2664563","display_name":"Q-learning","level":3,"score":0.421999990940094},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38920000195503235},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3361000120639801},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C2779295839","wikidata":"https://www.wikidata.org/wiki/Q3544090","display_name":"Punishment (psychology)","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C2779918689","wikidata":"https://www.wikidata.org/wiki/Q3771842","display_name":"Stimulus (psychology)","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.265500009059906},{"id":"https://openalex.org/C5570062","wikidata":"https://www.wikidata.org/wiki/Q3919817","display_name":"Behavioural sciences","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.2542000114917755},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25099998712539673}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3389/frobt.2025.1649154","is_oa":true,"landing_page_url":"https://doi.org/10.3389/frobt.2025.1649154","pdf_url":"https://www.frontiersin.org/journals/robotics-and-ai/articles/10.3389/frobt.2025.1649154/pdf","source":{"id":"https://openalex.org/S2595095599","display_name":"Frontiers in Robotics and AI","issn_l":"2296-9144","issn":["2296-9144"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Robotics and AI","raw_type":"journal-article"},{"id":"pmid:41080713","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41080713","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in robotics and AI","raw_type":null},{"id":"pmh:oai:doaj.org/article:015d7bdddf024f6db68be62d57da533e","is_oa":true,"landing_page_url":"https://doaj.org/article/015d7bdddf024f6db68be62d57da533e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Robotics and AI, Vol 12 (2025)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:11315608","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12507549","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:12507549","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12507549/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Front Robot AI","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3389/frobt.2025.1649154","is_oa":true,"landing_page_url":"https://doi.org/10.3389/frobt.2025.1649154","pdf_url":"https://www.frontiersin.org/journals/robotics-and-ai/articles/10.3389/frobt.2025.1649154/pdf","source":{"id":"https://openalex.org/S2595095599","display_name":"Frontiers in Robotics and AI","issn_l":"2296-9144","issn":["2296-9144"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Robotics and AI","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4414487421.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1535226523","https://openalex.org/W1642699591","https://openalex.org/W1970789124","https://openalex.org/W1989418985","https://openalex.org/W2007414406","https://openalex.org/W2043615441","https://openalex.org/W2069428670","https://openalex.org/W2155027007","https://openalex.org/W2169206416","https://openalex.org/W2528951757","https://openalex.org/W2612146718","https://openalex.org/W2736601468","https://openalex.org/W2799151646","https://openalex.org/W2990747716","https://openalex.org/W2999778183","https://openalex.org/W3041202696","https://openalex.org/W3101328236","https://openalex.org/W3106184835","https://openalex.org/W3111064853","https://openalex.org/W3164559980","https://openalex.org/W3200541323","https://openalex.org/W3213774989","https://openalex.org/W3216772467","https://openalex.org/W4205616158","https://openalex.org/W4210489512","https://openalex.org/W4214717370","https://openalex.org/W4225976907","https://openalex.org/W4226400653","https://openalex.org/W4229609137","https://openalex.org/W4284673391","https://openalex.org/W4365806381","https://openalex.org/W4381573739","https://openalex.org/W4386056879","https://openalex.org/W4386285856","https://openalex.org/W4387372443","https://openalex.org/W4390702324","https://openalex.org/W4394872716","https://openalex.org/W4400518895","https://openalex.org/W4404305238","https://openalex.org/W4413919390"],"related_works":[],"abstract_inverted_index":{"This":[0],"study":[1],"investigates":[2],"a":[3,102,125,173,202,206,262],"novel":[4],"nonlinear":[5,139],"update":[6,24,115],"rule":[7,25],"for":[8],"value":[9,188],"and":[10,66,91,116,209,237,251,258,279],"policy":[11],"functions":[12],"based":[13],"on":[14,124,198],"temporal":[15],"difference":[16],"(TD)":[17],"errors":[18],"in":[19,26,62,81,95,131,135,162,170,175],"reinforcement":[20],"learning":[21,82],"(RL).":[22],"The":[23],"standard":[27,151],"RL":[28,266],"states":[29],"that":[30,58,105,221,274],"the":[31,38,50,63,67,108,111,114,132,137,147,150,156,166,183,187,194,211,232,241,253,264,271,276],"TD":[32,64,117,178],"error":[33,65],"is":[34,160,180],"linearly":[35],"proportional":[36],"to":[37,84,88,142,172,228,239,281],"degree":[39,68,112,167],"of":[40,69,113,149,168,196,213,217],"updates,":[41,70],"treating":[42],"all":[43],"rewards":[44,236],"equally":[45],"without":[46],"any":[47],"bias.":[48],"On":[49],"other":[51],"hand,":[52],"recent":[53],"biological":[54,96],"studies":[55],"have":[56],"revealed":[57],"there":[59],"are":[60,86],"nonlinearities":[61,85],"biasing":[71],"policies":[72],"towards":[73],"being":[74],"either":[75],"optimistic":[76],"or":[77],"pessimistic.":[78],"Such":[79],"biases":[80],"due":[83],"expected":[87,254,272],"be":[89,143,225],"useful":[90],"intentionally":[92],"leftover":[93],"features":[94],"learning.":[97,285],"Therefore,":[98],"this":[99,120,218],"research":[100],"explores":[101],"theoretical":[103],"framework":[104,129,208],"can":[106,224],"leverage":[107],"nonlinearity":[109],"between":[110],"errors.":[118],"To":[119,191],"end,":[121],"we":[122,200],"focus":[123],"control":[126],"as":[127,182,244,246],"inference":[128],"utilized":[130],"previous":[133],"work,":[134],"which":[136,163],"uncomputable":[138],"term":[140],"needed":[141],"approximately":[144],"excluded":[145],"from":[146,231],"derivation":[148],"RL.":[152],"By":[153],"analyzing":[154],"it,":[155],"Weber\u2013Fechner":[157],"law":[158],"(WFL)":[159],"found,":[161],"perception":[164],"(i.e.,":[165,177,186],"updates)":[169],"response":[171],"change":[174],"stimulus":[176,184],"error)":[179],"attenuated":[181],"intensity":[185],"function)":[189],"increases.":[190],"numerically":[192],"demonstrate":[193],"utilities":[195,223,255,273],"WFL":[197,269],"RL,":[199],"propose":[201],"practical":[203],"implementation":[204,219],"using":[205],"reward\u2013punishment":[207],"modify":[210],"definition":[212],"optimality.":[214],"Further":[215],"analysis":[216],"reveals":[220],"two":[222],"expected:":[226],"i)":[227],"accelerate":[229,275],"escaping":[230],"situations":[233],"with":[234,268],"small":[235],"ii)":[238],"pursue":[240],"minimum":[242],"punishment":[243],"much":[245],"possible.":[247],"We":[248],"finally":[249],"investigate":[250],"discuss":[252],"through":[256],"simulations":[257],"robot":[259],"experiments.":[260],"As":[261],"result,":[263],"proposed":[265],"algorithm":[267],"shows":[270],"reward-maximizing":[277],"startup":[278],"continue":[280],"suppress":[282],"punishments":[283],"during":[284]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}