{"id":"https://openalex.org/W7127448103","doi":"https://doi.org/10.48550/arxiv.2602.00771","title":"Learning in Bayesian Stackelberg Games With Unknown Follower's Types","display_name":"Learning in Bayesian Stackelberg Games With Unknown Follower's Types","publication_year":2026,"publication_date":"2026-01-31","ids":{"openalex":"https://openalex.org/W7127448103","doi":"https://doi.org/10.48550/arxiv.2602.00771"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.00771","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","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/A5098623175","display_name":"Matteo Bollini","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bollini, Matteo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076607751","display_name":"Francesco Bacchiocchi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bacchiocchi, Francesco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124926591","display_name":"Samuel Coutts","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Coutts, Samuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018390908","display_name":"Matteo Castiglioni","orcid":"https://orcid.org/0000-0002-1070-6766"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Castiglioni, Matteo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039843107","display_name":"Alberto Marchesi","orcid":"https://orcid.org/0000-0002-8284-5757"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marchesi, Alberto","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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10750648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.7773000001907349,"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"}},"topics":[{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.7773000001907349,"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/T11031","display_name":"Game Theory and Applications","score":0.1906999945640564,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.004000000189989805,"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/regret","display_name":"Regret","score":0.8374999761581421},{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.7990999817848206},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.6230999827384949},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5792999863624573},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.5730000138282776},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5467000007629395},{"id":"https://openalex.org/keywords/bayesian-game","display_name":"Bayesian game","score":0.40779998898506165}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.8374999761581421},{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.7990999817848206},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.6230999827384949},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5792999863624573},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5730000138282776},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5467000007629395},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5461000204086304},{"id":"https://openalex.org/C200594392","wikidata":"https://www.wikidata.org/wiki/Q812529","display_name":"Bayesian game","level":4,"score":0.40779998898506165},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38769999146461487},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38339999318122864},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34599998593330383},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.31619998812675476},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.30239999294281006},{"id":"https://openalex.org/C2986087404","wikidata":"https://www.wikidata.org/wiki/Q15946010","display_name":"Online learning","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C31084985","wikidata":"https://www.wikidata.org/wiki/Q372650","display_name":"Common knowledge (logic)","level":5,"score":0.2874999940395355},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.2822999954223633},{"id":"https://openalex.org/C28901747","wikidata":"https://www.wikidata.org/wiki/Q177571","display_name":"Decision theory","level":2,"score":0.2632000148296356}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.00771","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.00771","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.00771","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.00771","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"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":{"We":[0,56],"study":[1],"online":[2],"learning":[3],"in":[4,72,100],"Bayesian":[5],"Stackelberg":[6],"games,":[7],"where":[8,147],"a":[9,14,112,156,160,165],"leader":[10,75,125],"repeatedly":[11],"interacts":[12],"with":[13,42,51],"follower":[15,87,105],"whose":[16],"unknown":[17,28],"private":[18],"type":[19,144,150],"is":[20,33,117,151],"independently":[21],"drawn":[22],"at":[23,132],"each":[24,136],"round":[25],"from":[26],"an":[27,47],"probability":[29],"distribution.":[30],"The":[31],"goal":[32],"to":[34,44,62,95],"design":[35],"algorithms":[36],"that":[37,163],"minimize":[38],"the":[39,54,59,63,68,74,81,85,96,102,124,128,133,142,148,171],"leader's":[40],"regret":[41,166],"respect":[43],"always":[45],"playing":[46],"optimal":[48],"commitment":[49],"computed":[50],"knowledge":[52],"of":[53,65,104,135,167],"game.":[55],"consider,":[57],"for":[58],"first":[60],"time":[61],"best":[64,130],"our":[66],"knowledge,":[67],"most":[69],"realistic":[70],"case":[71,99],"which":[73,101],"does":[76],"not":[77],"know":[78],"anything":[79],"about":[80],"follower's":[82,129,149],"types,":[83],"i.e.,":[84,122],"possible":[86],"payoffs.":[88],"This":[89],"raises":[90],"considerable":[91],"additional":[92],"challenges":[93],"compared":[94],"commonly":[97],"studied":[98],"payoffs":[103],"types":[106],"are":[107],"known.":[108],"First,":[109],"we":[110,139,158],"prove":[111],"strong":[113],"negative":[114],"result:":[115],"no-regret":[116,161],"unattainable":[118],"under":[119],"action":[120],"feedback,":[121],"when":[123,169],"only":[126],"observes":[127],"response":[131],"end":[134],"round.":[137],"Thus,":[138],"focus":[140],"on":[141,173],"easier":[143],"feedback":[145],"model,":[146],"also":[152],"revealed.":[153],"In":[154],"such":[155],"setting,":[157],"propose":[159],"algorithm":[162],"achieves":[164],"$\\widetilde{O}(\\sqrt{T})$,":[168],"ignoring":[170],"dependence":[172],"other":[174],"parameters.":[175]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-02-04T00:00:00"}