{"id":"https://openalex.org/W4389799550","doi":"https://doi.org/10.1109/lcsys.2023.3343439","title":"Rates of Convergence in a Class of Native Spaces for Reinforcement Learning and Control","display_name":"Rates of Convergence in a Class of Native Spaces for Reinforcement Learning and Control","publication_year":2023,"publication_date":"2023-12-15","ids":{"openalex":"https://openalex.org/W4389799550","doi":"https://doi.org/10.1109/lcsys.2023.3343439"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2023.3343439","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2023.3343439","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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 Control Systems Letters","raw_type":"journal-article"},"type":"article","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/A5092885758","display_name":"Ali Bouland","orcid":"https://orcid.org/0009-0002-1383-316X"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ali Bouland","raw_affiliation_strings":["Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA"],"raw_orcid":"https://orcid.org/0009-0002-1383-316X","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104298526","display_name":"Shengyuan Niu","orcid":null},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shengyuan Niu","raw_affiliation_strings":["Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057872436","display_name":"Sai Tej Paruchuri","orcid":"https://orcid.org/0000-0003-2372-3888"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sai Tej Paruchuri","raw_affiliation_strings":["Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA"],"raw_orcid":"https://orcid.org/0000-0003-2372-3888","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023864855","display_name":"Andrew J. Kurdila","orcid":"https://orcid.org/0000-0002-9042-5146"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Kurdila","raw_affiliation_strings":["Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA"],"raw_orcid":"https://orcid.org/0000-0002-9042-5146","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102791907","display_name":"John A. Burns","orcid":"https://orcid.org/0000-0003-1840-927X"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Burns","raw_affiliation_strings":["Department of Mathematics, Virginia Tech, Blacksburg, VA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Virginia Tech, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051077845","display_name":"Eugenio Schuster","orcid":"https://orcid.org/0000-0001-7703-6771"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eugenio Schuster","raw_affiliation_strings":["Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA"],"raw_orcid":"https://orcid.org/0000-0001-7703-6771","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2345,"currency":"USD","value_usd":2345},"apc_paid":null,"fwci":0.2551,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.50441109,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8","issue":null,"first_page":"55","last_page":"60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9606000185012817,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9569000005722046,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.7686160206794739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6649768352508545},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6483619809150696},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.6067253351211548},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5708778500556946},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.5617218017578125},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5321584939956665},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5158588290214539},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5122577548027039},{"id":"https://openalex.org/keywords/function-space","display_name":"Function space","score":0.5100544095039368},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49930739402770996},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.48790284991264343},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.47591596841812134},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.44257792830467224},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4368407130241394},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4221140146255493},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27824798226356506},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.27694636583328247},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19897446036338806},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09267014265060425},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06941214203834534}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.7686160206794739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6649768352508545},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6483619809150696},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.6067253351211548},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5708778500556946},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5617218017578125},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5321584939956665},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5158588290214539},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5122577548027039},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.5100544095039368},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49930739402770996},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.48790284991264343},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.47591596841812134},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.44257792830467224},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4368407130241394},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4221140146255493},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27824798226356506},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27694636583328247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19897446036338806},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09267014265060425},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06941214203834534},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lcsys.2023.3343439","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2023.3343439","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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 Control Systems Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6499999761581421,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W560518094","https://openalex.org/W1486164486","https://openalex.org/W1570089119","https://openalex.org/W1983523797","https://openalex.org/W1988793248","https://openalex.org/W1994655188","https://openalex.org/W2005728609","https://openalex.org/W2047090868","https://openalex.org/W2068328804","https://openalex.org/W2108286682","https://openalex.org/W2772589676","https://openalex.org/W2800330509","https://openalex.org/W2904727539","https://openalex.org/W3104395920","https://openalex.org/W3190367256","https://openalex.org/W4211049957","https://openalex.org/W4241431509","https://openalex.org/W4250739957","https://openalex.org/W4292232969","https://openalex.org/W4386794600","https://openalex.org/W6856725180"],"related_works":["https://openalex.org/W2018264451","https://openalex.org/W2591253179","https://openalex.org/W2053635157","https://openalex.org/W4234882900","https://openalex.org/W2908964587","https://openalex.org/W2982110994","https://openalex.org/W1699343347","https://openalex.org/W2053054589","https://openalex.org/W2285605129","https://openalex.org/W1991395770"],"abstract_inverted_index":{"This":[0],"letter":[1],"studies":[2],"convergence":[3,38,104],"rates":[4,36],"for":[5,41],"some":[6,97],"value":[7,60,108],"function":[8,61],"approximations":[9,48,65,106],"that":[10,45,49],"arise":[11],"in":[12,28,51,59,68],"a":[13,29,89],"collection":[14],"of":[15,32,37,70,77,105,107],"reproducing":[16],"kernel":[17],"Hilbert":[18],"spaces":[19],"(RKHS)${\\mathrm{":[20],"H}}(\\Omega)$.":[21,85],"By":[22],"casting":[23],"an":[24],"optimal":[25],"control":[26,63],"problem":[27],"specific":[30],"class":[31],"native":[33,83],"spaces,":[34],"strong":[35],"are":[39,66],"derived":[40,67],"the":[42,75,82,103],"operator":[43],"equation":[44],"enables":[46],"offline":[47],"appear":[50],"policy":[52],"iteration.":[53],"Explicit":[54],"upper":[55],"bounds":[56,87],"on":[57],"error":[58],"and":[62,94],"law":[64],"terms":[69],"power":[71],"function$\\mathcal":[72],"{P}_{\\mathrm{":[73],"H,N}}$for":[74],"space":[76],"finite":[78],"dimensional":[79],"approximants$\\rm":[80],"H_{N}$in":[81],"space${\\mathrm{":[84],"These":[86],"exhibit":[88],"distinctive":[90],"geometric":[91],"nature,":[92],"refine":[93],"build":[95],"upon":[96],"well-known,":[98],"now":[99],"classical":[100],"results":[101],"concerning":[102],"functions.":[109]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
