{"id":"https://openalex.org/W7159653862","doi":"https://doi.org/10.48550/arxiv.2604.28005","title":"Kernelized Advantage Estimation: From Nonparametric Statistics to LLM Reasoning","display_name":"Kernelized Advantage Estimation: From Nonparametric Statistics to LLM Reasoning","publication_year":2026,"publication_date":"2026-04-30","ids":{"openalex":"https://openalex.org/W7159653862","doi":"https://doi.org/10.48550/arxiv.2604.28005"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.28005","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.28005","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.28005","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125129142","display_name":"Shijin Gong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gong, Shijin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134968786","display_name":"Kai Ye","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ye, Kai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134980931","display_name":"Jin Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Jin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134974529","display_name":"Xinyu Zhang (14029)","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Xinyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134986610","display_name":"Hongyi Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Hongyi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134992122","display_name":"Chengchun Shi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Chengchun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.32089999318122864,"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":0.32089999318122864,"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/T10028","display_name":"Topic Modeling","score":0.15629999339580536,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.09860000014305115,"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/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.6345000267028809},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.6270999908447266},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.550000011920929},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5386000275611877},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.47839999198913574},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.47760000824928284},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.47609999775886536},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.47530001401901245},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.4546999931335449}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6559000015258789},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.6345000267028809},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.6270999908447266},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5767999887466431},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.550000011920929},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5497999787330627},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5386000275611877},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.47839999198913574},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.47760000824928284},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.47609999775886536},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.47530001401901245},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.4546999931335449},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4196000099182129},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.3560999929904938},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.33309999108314514},{"id":"https://openalex.org/C27406209","wikidata":"https://www.wikidata.org/wiki/Q6394203","display_name":"Kernel smoother","level":5,"score":0.3174000084400177},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3111000061035156},{"id":"https://openalex.org/C89249532","wikidata":"https://www.wikidata.org/wiki/Q7912758","display_name":"Value network","level":3,"score":0.30250000953674316},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3001999855041504},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.2822999954223633},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C65660741","wikidata":"https://www.wikidata.org/wiki/Q3952743","display_name":"Score","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.2515000104904175},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.28005","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.28005","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.28005","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.28005","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Recent":[0],"advances":[1],"in":[2,44,131],"large":[3,87],"language":[4],"models":[5],"(LLMs)":[6],"have":[7,23],"increasingly":[8],"relied":[9],"on":[10,30,126],"reinforcement":[11],"learning":[12,42],"(RL)":[13],"to":[14,35,46,172,207],"improve":[15],"their":[16],"reasoning":[17,90,109,138],"capabilities.":[18],"Three":[19],"types":[20],"of":[21,40,50,89,137],"approaches":[22],"been":[24],"widely":[25],"adopted:":[26],"The":[27,68,103],"first":[28],"relies":[29],"a":[31,59,72,86,107,127,134,180],"deep":[32],"neural":[33],"network":[34,61,74],"estimate":[36],"the":[37,41,48,51,77,188],"value":[38,60,73,78,96,184,202],"function":[39,79,97,185],"policy":[43,52,153,190,209],"order":[45],"reduce":[47],"variance":[49],"gradient.":[53],"However,":[54,83],"estimating":[55],"and":[56,65,169,187,193,203],"maintaining":[57],"such":[58],"incurs":[62],"substantial":[63],"computational":[64,115],"memory":[66],"overhead.":[67],"second":[69],"avoids":[70],"training":[71],"by":[75],"approximating":[76],"using":[80],"sample":[81,121],"averages.":[82],"it":[84,100],"samples":[85,105],"number":[88,136],"traces":[91,139],"per":[92,111,143],"prompt":[93],"for":[94,151,183],"accurate":[95,201],"approximation,":[98],"making":[99],"computationally":[101,168],"expensive.":[102],"third":[104],"only":[106,133],"single":[108],"trajectory":[110],"prompt,":[112,144],"which":[113,132,165],"reduces":[114],"cost":[116],"but":[117],"suffers":[118],"from":[119],"poor":[120],"efficiency.":[122],"This":[123],"paper":[124],"focuses":[125],"practical,":[128],"resource-constrained":[129],"setting":[130],"small":[135],"can":[140],"be":[141],"sampled":[142],"while":[145],"low-variance":[146],"gradient":[147,204],"estimation":[148,186],"remains":[149],"essential":[150],"high-quality":[152],"learning.":[154],"To":[155],"address":[156],"this":[157],"challenge,":[158],"we":[159],"bring":[160],"classical":[161],"nonparametric":[162],"statistical":[163],"methods,":[164],"are":[166],"both":[167],"statistically":[170],"efficient,":[171],"LLM":[173],"reasoning.":[174],"We":[175],"employ":[176],"kernel":[177],"smoothing":[178],"as":[179],"concrete":[181],"example":[182],"subsequent":[189],"optimization.":[191,210],"Numerical":[192],"theoretical":[194],"results":[195],"demonstrate":[196],"that":[197],"our":[198],"proposal":[199],"achieves":[200],"estimation,":[205],"leading":[206],"improved":[208]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-02T00:00:00"}