{"id":"https://openalex.org/W7129237314","doi":"https://doi.org/10.48550/arxiv.2602.14868","title":"Goldilocks RL: Tuning Task Difficulty to Escape Sparse Rewards for Reasoning","display_name":"Goldilocks RL: Tuning Task Difficulty to Escape Sparse Rewards for Reasoning","publication_year":2026,"publication_date":"2026-02-16","ids":{"openalex":"https://openalex.org/W7129237314","doi":"https://doi.org/10.48550/arxiv.2602.14868"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.14868","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114653629","display_name":"Ilia Mahrooghi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mahrooghi, Ilia","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126222789","display_name":"Aryo Lotfi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lotfi, Aryo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126273815","display_name":"Emmanuel Abbe","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abbe, Emmanuel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5114653629"],"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/T10028","display_name":"Topic Modeling","score":0.2551000118255615,"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/T10028","display_name":"Topic Modeling","score":0.2551000118255615,"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/T11902","display_name":"Intelligent Tutoring Systems and Adaptive Learning","score":0.1712999939918518,"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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.08470000326633453,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/goldilocks-principle","display_name":"Goldilocks principle","score":0.9114999771118164},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.6923999786376953},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.6270999908447266},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.5315999984741211},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.48159998655319214},{"id":"https://openalex.org/keywords/task-analysis","display_name":"Task analysis","score":0.367000013589859},{"id":"https://openalex.org/keywords/training-set","display_name":"Training set","score":0.30309998989105225}],"concepts":[{"id":"https://openalex.org/C177321328","wikidata":"https://www.wikidata.org/wiki/Q13580479","display_name":"Goldilocks principle","level":2,"score":0.9114999771118164},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7706999778747559},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.6923999786376953},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.6270999908447266},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5315999984741211},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.512499988079071},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.48159998655319214},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.44119998812675476},{"id":"https://openalex.org/C175154964","wikidata":"https://www.wikidata.org/wiki/Q380077","display_name":"Task analysis","level":3,"score":0.367000013589859},{"id":"https://openalex.org/C107457646","wikidata":"https://www.wikidata.org/wiki/Q207434","display_name":"Human\u2013computer interaction","level":1,"score":0.35910001397132874},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C171268870","wikidata":"https://www.wikidata.org/wiki/Q1486676","display_name":"GRASP","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C2982912361","wikidata":"https://www.wikidata.org/wiki/Q1851867","display_name":"Mental model","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C77967617","wikidata":"https://www.wikidata.org/wiki/Q4677561","display_name":"Active learning (machine learning)","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C47177190","wikidata":"https://www.wikidata.org/wiki/Q207137","display_name":"Curriculum","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.14868","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.14868","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.14868","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":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.14868","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.4152076542377472}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Reinforcement":[0],"learning":[1,39],"has":[2],"emerged":[3],"as":[4,26],"a":[5,54,66],"powerful":[6],"paradigm":[7],"for":[8,53,79,91],"unlocking":[9],"reasoning":[10],"capabilities":[11],"in":[12],"large":[13],"language":[14],"models.":[15],"However,":[16],"relying":[17],"on":[18,48,118],"sparse":[19],"rewards":[20],"makes":[21],"this":[22,43],"process":[23],"highly":[24],"sample-inefficient,":[25],"models":[27,140],"must":[28],"navigate":[29],"vast":[30],"search":[31],"spaces":[32],"with":[33,111,142],"minimal":[34],"feedback.":[35],"While":[36],"classic":[37],"curriculum":[38],"aims":[40,73],"to":[41,74,125],"mitigate":[42],"by":[44],"ordering":[45,52],"data":[46,69,134],"based":[47],"complexity,":[49],"the":[50,80,92,109,115,121,126,137,146],"right":[51],"specific":[55],"model":[56,85],"is":[57],"often":[58],"unclear.":[59],"To":[60],"address":[61],"this,":[62],"we":[63],"propose":[64],"Goldilocks,":[65],"novel":[67],"teacher-driven":[68],"sampling":[70,135],"strategy":[71],"that":[72,97],"predict":[75],"each":[76],"question's":[77],"difficulty":[78,90],"student":[81,93,110],"model.":[82],"The":[83],"teacher":[84,122],"selects":[86],"questions":[87,96],"of":[88,139],"appropriate":[89],"model,":[94],"i.e.,":[95],"are":[98],"neither":[99],"too":[100,103],"easy":[101],"nor":[102],"hard":[104],"(Goldilocks":[105],"principle),":[106],"while":[107],"training":[108],"GRPO.":[112],"By":[113],"leveraging":[114],"student's":[116,127],"performance":[117,138],"seen":[119],"samples,":[120],"continuously":[123],"adapts":[124],"evolving":[128],"abilities.":[129],"On":[130],"OpenMathReasoning":[131],"dataset,":[132],"Goldilocks":[133],"improves":[136],"trained":[141],"standard":[143],"GRPO":[144],"under":[145],"same":[147],"compute":[148],"budget.":[149]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-18T00:00:00"}
