{"id":"https://openalex.org/W7138103454","doi":"https://doi.org/10.1609/aaai.v40i29.39632","title":"Parameter-free Optimal Rates for Nonlinear Semi-Norm Contractions with Applications to Q-Learning","display_name":"Parameter-free Optimal Rates for Nonlinear Semi-Norm Contractions with Applications to Q-Learning","publication_year":2026,"publication_date":"2026-03-14","ids":{"openalex":"https://openalex.org/W7138103454","doi":"https://doi.org/10.1609/aaai.v40i29.39632"},"language":null,"primary_location":{"id":"doi:10.1609/aaai.v40i29.39632","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v40i29.39632","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/39632/43593","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ojs.aaai.org/index.php/AAAI/article/download/39632/43593","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111136248","display_name":"Ankur Naskar","orcid":null},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ankur Naskar","raw_affiliation_strings":["Indian Institute of Science, Bengaluru"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Science, Bengaluru","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047138399","display_name":"Gugan Thoppe","orcid":"https://orcid.org/0000-0001-5066-6589"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Gugan Thoppe","raw_affiliation_strings":["Indian Institute of Science, Bengaluru"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Science, Bengaluru","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5129723142","display_name":"Vijay Kumar Gupta","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vijay Gupta","raw_affiliation_strings":["Purdue University"],"affiliations":[{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111136248"],"corresponding_institution_ids":["https://openalex.org/I59270414"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.32334047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"29","first_page":"24495","last_page":"24503"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.5196999907493591,"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":0.5196999907493591,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.09350000321865082,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.0502999983727932,"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/nonlinear-system","display_name":"Nonlinear system","score":0.732699990272522},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6711000204086304},{"id":"https://openalex.org/keywords/asynchronous-communication","display_name":"Asynchronous communication","score":0.5794000029563904},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5047000050544739},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5044999718666077},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5011000037193298},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.45329999923706055},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.4514000117778778}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.732699990272522},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6711000204086304},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6201000213623047},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.5794000029563904},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5694000124931335},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5047000050544739},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5044999718666077},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5011000037193298},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.45329999923706055},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.4514000117778778},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.37279999256134033},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.3569999933242798},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3546000123023987},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3142000138759613},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.2759000062942505},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1609/aaai.v40i29.39632","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v40i29.39632","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/39632/43593","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1609/aaai.v40i29.39632","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v40i29.39632","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/39632/43593","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7138103454.pdf","grobid_xml":"https://content.openalex.org/works/W7138103454.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Algorithms":[0],"for":[1,19,82],"solving":[2],"nonlinear":[3,52],"fixed-point":[4],"equations---such":[5],"as":[6,46],"average-reward":[7,86],"Q-learning":[8,83],"and":[9,54,87,108,112,115],"TD-learning---often":[10],"involve":[11],"semi-norm":[12],"contractions.":[13],"Achieving":[14],"parameter-free":[15,78],"optimal":[16,80],"convergence":[17],"rates":[18,81],"these":[20],"methods":[21],"via":[22],"Polyak\u2013Ruppert":[23],"averaging":[24],"has":[25],"remained":[26],"elusive,":[27],"largely":[28],"due":[29],"to":[30],"the":[31,43,57,61,65,76,94],"non-monotonicity":[32],"of":[33,67],"such":[34],"semi-norms.":[35],"We":[36],"close":[37],"this":[38],"gap":[39],"by":[40,59],"(i.)":[41],"recasting":[42],"averaged":[44],"error":[45],"a":[47,51,68,101],"linear":[48],"recursion":[49],"involving":[50],"perturbation,":[53],"(ii.)":[55],"taming":[56],"nonlinearity":[58],"coupling":[60],"semi-norm's":[62],"contraction":[63],"with":[64],"monotonicity":[66],"suitably":[69],"induced":[70],"norm.":[71],"Our":[72],"main":[73],"result":[74,98],"yields":[75],"first":[77],"~O(1/\u221at)":[79],"in":[84],"both":[85,106],"exponentially":[88],"discounted":[89],"settings,":[90],"where":[91],"t":[92],"denotes":[93],"iteration":[95],"index.":[96],"The":[97],"applies":[99],"within":[100],"broad":[102],"framework":[103],"that":[104],"accommodates":[105],"synchronous":[107],"asynchronous":[109],"updates,":[110],"single-agent":[111],"distributed":[113],"deployments,":[114],"data":[116],"streams":[117],"obtained":[118],"from":[119],"either":[120],"simulators":[121],"or":[122],"along":[123],"Markovian":[124],"trajectories.":[125]},"counts_by_year":[],"updated_date":"2026-03-20T20:47:17.329874","created_date":"2026-03-18T00:00:00"}
