{"id":"https://openalex.org/W7204279360","doi":"https://doi.org/10.48550/arxiv.2608.24167","title":"From Relaxed Indexability to Exact Indexability: A $t$-Step Approach for Partially Observable Restless Bandits","display_name":"From Relaxed Indexability to Exact Indexability: A $t$-Step Approach for Partially Observable Restless Bandits","publication_year":2026,"publication_date":"2026-08-25","ids":{"openalex":"https://openalex.org/W7204279360","doi":"https://doi.org/10.48550/arxiv.2608.24167"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.24167","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24167","pdf_url":"https://arxiv.org/pdf/2608.24167","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2608.24167","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151045140","display_name":"Keqin Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Keqin","raw_affiliation_strings":["School of Mathematics and Physics Xi'an Jiaotong-Liverpool University Suzhou 215123 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics Xi'an Jiaotong-Liverpool University Suzhou 215123 , China","institution_ids":["https://openalex.org/I69356397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002981711","display_name":"Qizhen Jia","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia, Qizhen","raw_affiliation_strings":["School of Mathematics and Physics Xi'an Jiaotong-Liverpool University Suzhou 215123 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics Xi'an Jiaotong-Liverpool University Suzhou 215123 , China","institution_ids":["https://openalex.org/I69356397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I69356397"],"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9980000257492065,"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":0.9980000257492065,"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/T12288","display_name":"Optimization and Search Problems","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.00039999998989515007,"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/multi-armed-bandits","display_name":"multi-armed bandits","score":0.6729999780654907}],"concepts":[{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.8151999711990356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6697999835014343},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5950999855995178},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5619000196456909},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.5572999715805054},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5005999803543091},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4406000077724457},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3614000082015991},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3612000048160553},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3483000099658966},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.2971000075340271},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C64413873","wikidata":"https://www.wikidata.org/wiki/Q21005","display_name":"Threshold limit value","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.24167","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24167","pdf_url":"https://arxiv.org/pdf/2608.24167","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.24167","doi":"https://doi.org/10.48550/arxiv.2608.24167","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.24167","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.24167","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24167","pdf_url":"https://arxiv.org/pdf/2608.24167","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/W7204279360.pdf","grobid_xml":"https://content.openalex.org/works/W7204279360.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2044375425","https://openalex.org/W2998102890","https://openalex.org/W4311632474","https://openalex.org/W4383605037"],"related_works":["https://openalex.org/W4312460289","https://openalex.org/W7171503792","https://openalex.org/W4409498162","https://openalex.org/W4315489038","https://openalex.org/W3192054687","https://openalex.org/W2800455436","https://openalex.org/W2298667432","https://openalex.org/W4226000026","https://openalex.org/W3095887231","https://openalex.org/W4295184151"],"abstract_inverted_index":{"Whittle":[0,55,153,161,168],"index":[1,162,185,194],"policies":[2,220],"offer":[3],"a":[4,21,48,52,63,80],"scalable":[5],"method":[6],"for":[7,71,116],"restless":[8],"multi-armed":[9],"bandits,":[10],"but":[11],"under":[12,97],"partial":[13],"observability":[14],"even":[15],"determining":[16],"the":[17,42,58,89,94,104,110,122,128,151,158,166,189,214,223,230],"indifference":[18],"subsidy":[19,87],"at":[20,199,203],"single":[22],"belief":[23],"requires":[24],"solving":[25],"an":[26,143,147,206],"infinite-horizon":[27],"belief-state":[28],"problem":[29],"with":[30,182,209,238],"no":[31],"closed-form":[32,53],"value":[33,100],"function.":[34],"Liu":[35,114],"[10]":[36],"addresses":[37],"this":[38,77],"difficulty":[39],"by":[40,93],"linearizing":[41],"unknown":[43],"decision":[44,130],"boundary,":[45],"leading":[46],"to":[47,79,165,188,201,229],"linear":[49,111],"system":[50],"and":[51,67,108,126,145,226],"approximate":[54,160],"index.":[56],"However,":[57],"resulting":[59],"threshold":[60,83,90,105,112,219],"uses":[61],"only":[62],"one-step":[64,224],"active--passive":[65],"comparison":[66],"does":[68,138],"not":[69,139],"account":[70],"longer-horizon":[72],"continuation":[73],"values.":[74],"We":[75],"extend":[76],"framework":[78,137],"\\emph{$t$-step":[81],"lookahead":[82],"policy}.":[84],"For":[85],"each":[86],"$m$,":[88],"is":[91,106],"defined":[92],"active-minus-passive":[95],"advantage":[96],"$t$-step":[98,159],"finite-horizon":[99],"iteration.":[101],"At":[102],"$t=1$,":[103],"$m$-independent":[107],"recovers":[109,213],"of":[113],"[10];":[115],"$t>1$,":[117],"it":[118],"becomes":[119],"subsidy-dependent":[120],"through":[121],"induced":[123],"first-crossing":[124],"structure":[125],"tracks":[127],"exact":[129,167,215],"boundary":[131],"more":[132],"closely.":[133],"The":[134,192],"proposed":[135,190],"algorithmic":[136],"require":[140],"indexability":[141,148],"as":[142],"input":[144],"includes":[146],"verification.":[149],"Under":[150],"original":[152],"indexability,":[154],"we":[155],"prove":[156],"that":[157],"converges":[163],"geometrically":[164],"index,":[169],"\\[":[170],"|\\widehat":[171],"W_t(\u03c9)-W(\u03c9)|=O(\u03b2^t).":[172],"\\]":[173],"Numerically,":[174],"all":[175],"2,715":[176],"tested":[177],"three-state":[178],"instances":[179],"are":[180],"verified":[181],"computable":[183],"priority":[184],"functions":[186],"according":[187],"criterion.":[191],"P95":[193],"error":[195],"decreases":[196],"from":[197],"$2.18\\times10^{-2}$":[198],"$t=1$":[200],"$8.93\\times10^{-4}$":[202],"$t=8$.":[204],"In":[205],"exact-comparable":[207],"instance":[208],"$\u03b2=0.9999$,":[210],"$t=2$":[211],"already":[212],"Whittle-index":[216],"ordering.":[217],"Moderate-depth":[218],"also":[221],"outperform":[222],"baseline":[225],"remain":[227],"close":[228],"optimal":[231],"dynamic-programming":[232],"benchmark,":[233],"while":[234],"runtime":[235],"grows":[236],"mildly":[237],"$t$.":[239]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-27T00:00:00"}
