{"id":"https://openalex.org/W7214905810","doi":"https://doi.org/10.48550/arxiv.2609.36945","title":"Fine-Tuning on Self-Generated and Reward-Weighted Data: Learning Dynamics, Convergence Rates, and Benefits of Off-Policyness","display_name":"Fine-Tuning on Self-Generated and Reward-Weighted Data: Learning Dynamics, Convergence Rates, and Benefits of Off-Policyness","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214905810","doi":"https://doi.org/10.48550/arxiv.2609.36945"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36945","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36945","pdf_url":"https://arxiv.org/pdf/2609.36945","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.36945","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153632159","display_name":"Zhiwei Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Zhiwei","raw_affiliation_strings":["Department of Mathematical Sciences Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153682098","display_name":"Yanxi Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I45928872","display_name":"Alibaba Group (China)","ror":"https://ror.org/00k642b80","country_code":"CN","type":"company","lineage":["https://openalex.org/I45928872"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Yanxi","raw_affiliation_strings":["Alibaba Group"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alibaba Group","institution_ids":["https://openalex.org/I45928872"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153601231","display_name":"Yaliang Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I45928872","display_name":"Alibaba Group (China)","ror":"https://ror.org/00k642b80","country_code":"CN","type":"company","lineage":["https://openalex.org/I45928872"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Yaliang","raw_affiliation_strings":["Alibaba Group"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alibaba Group","institution_ids":["https://openalex.org/I45928872"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153677149","display_name":"Bolin Ding","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ding, Bolin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.6636000275611877,"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":0.6636000275611877,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.33399999141693115,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.0003000000142492354,"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/off-policy-learning","display_name":"off-policy learning","score":0.5649999976158142},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.7440000176429749},{"id":"https://openalex.org/keywords/multi-armed-bandits","display_name":"multi-armed bandits","score":0.8050000071525574},{"id":"https://openalex.org/keywords/kullback-leibler-divergence","display_name":"Kullback-Leibler divergence","score":0.8140000104904175}],"concepts":[{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.7897999882698059},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7045999765396118},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.6305999755859375},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49320000410079956},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4867999851703644},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.47600001096725464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4453999996185303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4447999894618988},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4262000024318695},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.3921000063419342},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3427000045776367},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.3264000117778778},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2863999903202057},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.26919999718666077},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.25940001010894775},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.2551000118255615},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36945","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36945","pdf_url":"https://arxiv.org/pdf/2609.36945","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.36945","doi":"https://doi.org/10.48550/arxiv.2609.36945","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36945","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36945","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36945","pdf_url":"https://arxiv.org/pdf/2609.36945","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214905810.pdf","grobid_xml":"https://content.openalex.org/works/W7214905810.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W2736601468","https://openalex.org/W4398795017","https://openalex.org/W4405766390","https://openalex.org/W4406774573","https://openalex.org/W4415309873","https://openalex.org/W4415330145","https://openalex.org/W6959934489","https://openalex.org/W7125817288","https://openalex.org/W7133192525","https://openalex.org/W7161006596"],"related_works":["https://openalex.org/W6910652885","https://openalex.org/W4361865079","https://openalex.org/W3177476039","https://openalex.org/W7196992494","https://openalex.org/W4414989703","https://openalex.org/W4405281200","https://openalex.org/W7160983503","https://openalex.org/W3170697419","https://openalex.org/W7128806247","https://openalex.org/W7204966963"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,32,92,104,124,149,184,188,206,219,236,271,279,283],"learning":[3,48],"dynamics":[4],"of":[5,22,107,127,190,208,222,238,285],"fine-tuning":[6],"a":[7,19,61,117,136,153,239,246,250,261,267],"policy":[8,54,186,248],"model":[9],"on":[10,18],"self-generated":[11],"and":[12,46,57,167,273],"reward-weighted":[13,155],"data,":[14],"with":[15,161,249,266],"particular":[16],"focus":[17],"generalized":[20],"version":[21],"REINFORCE":[23],"--":[24,29],"referred":[25],"to":[26,71,87,152,183,278],"as":[27,69,135,187],"RE(S)":[28,121,179,223,265],"that":[30,122,218],"updates":[31,193],"rollout":[33,93,156,191],"distribution":[34,94,192],"once":[35],"every":[36],"$S":[37,128],"\\ge":[38,129],"1$":[39],"gradient":[40,55,145,209],"steps.":[41],"Prior":[42],"work":[43],"in":[44,75,287],"bandits":[45,160],"reinforcement":[47],"has":[49,85],"developed":[50],"rich":[51],"theory":[52,119],"for":[53,103,120,147,175,260],"methods,":[56],"on-policy":[58],"sampling":[59],"(i.e.,":[60],"small":[62,251],"$S$,":[63,178],"ideally":[64],"$1$)":[65],"is":[66,95],"often":[67],"viewed":[68],"crucial":[70],"their":[72],"success;":[73],"yet":[74],"prominent":[76],"application":[77],"like":[78],"post-training":[79],"large":[80],"language":[81],"models,":[82],"reward-guided":[83],"self-training":[84],"proved":[86],"be":[88,133],"effective":[89],"even":[90],"when":[91,243],"updated":[96],"infrequently,":[97],"but":[98],"theoretical":[99],"understanding":[100],"remains":[101],"limited":[102],"convergence":[105,182,230,277],"properties":[106],"these":[108,113],"off-policy":[109],"methods.":[110],"To":[111],"bridge":[112],"gaps,":[114],"we":[115,212],"develop":[116],"unified":[118],"covers":[123],"full":[125],"spectrum":[126],"1$:":[130],"it":[131],"can":[132],"interpreted":[134],"stage-wise":[137],"optimization":[138],"process,":[139],"where":[140,203],"each":[141],"stage":[142],"takes":[143],"$S$":[144,233,269],"steps":[146],"minimizing":[148],"Kullback-Leibler":[150],"distance":[151],"fixed":[154,177],"distribution.":[157],"For":[158],"multi-arm":[159],"softmax":[162],"policies,":[163],"our":[164],"in-depth":[165],"analysis":[166],"numerical":[168],"experiments":[169],"reveal":[170],"three":[171],"key":[172],"findings:":[173],"(1)":[174],"any":[176],"enjoys":[180],"global":[181,280],"optimal":[185],"number":[189,207],"$B":[194],"=":[195],"\\lfloor":[196],"T":[197],"/":[198,228],"S":[199],"\\rfloor":[200],"\\rightarrow":[201],"\\infty$,":[202],"$T$":[204],"denotes":[205],"steps;":[210],"(2)":[211],"prove":[213],"tight":[214],"two-sided":[215],"bounds":[216],"showing":[217],"suboptimality":[220],"gap":[221],"achieves":[224,274],"an":[225],"asymptotic":[226],"$\u0398(1":[227],"T)$":[229],"rate,":[231],"while":[232],"only":[234],"affects":[235],"length":[237],"burn-in":[240],"phase;":[241],"(3)":[242],"initialized":[244],"at":[245],"weak":[247],"optimal-action":[252],"probability,":[253],"RE(1)":[254],"gets":[255],"trapped":[256],"around":[257],"suboptimal":[258],"policies":[259],"long":[262],"period,":[263],"whereas":[264],"suitable":[268],"avoids":[270],"detour":[272],"significantly":[275],"faster":[276],"optimum,":[281],"highlighting":[282],"benefits":[284],"off-policyness":[286],"this":[288],"case.":[289]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}
