{"id":"https://openalex.org/W7151027473","doi":"https://doi.org/10.48550/arxiv.2604.02727","title":"Data-Driven Synthesis of Probabilistic Controlled Invariant Sets for Linear MDPs","display_name":"Data-Driven Synthesis of Probabilistic Controlled Invariant Sets for Linear MDPs","publication_year":2026,"publication_date":"2026-04-03","ids":{"openalex":"https://openalex.org/W7151027473","doi":"https://doi.org/10.48550/arxiv.2604.02727"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.02727","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02727","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.02727","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025704398","display_name":"Kazumune Hashimoto","orcid":"https://orcid.org/0000-0002-9376-5760"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hashimoto, Kazumune","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019016020","display_name":"Shunki Kimura","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kimura, Shunki","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132605605","display_name":"Kazunobu Serizawa","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Serizawa, Kazunobu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133028858","display_name":"Junya Ikemoto","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ikemoto, Junya","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133037099","display_name":"Yulong Gao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gao, Yulong","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133031298","display_name":"Kai Cai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cai, Kai","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5025704398"],"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.4072999954223633,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.4072999954223633,"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/T10142","display_name":"Formal Methods in Verification","score":0.19300000369548798,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.12349999696016312,"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.6908000111579895},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.6489999890327454},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5306000113487244},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5228000283241272},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.510699987411499},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.45210000872612},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.43689998984336853},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.3677000105381012},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.366100013256073}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6908000111579895},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.6489999890327454},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5306000113487244},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5228000283241272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5210000276565552},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.510699987411499},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47850000858306885},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.45210000872612},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.43689998984336853},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.3677000105381012},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.366100013256073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36059999465942383},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3458999991416931},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3043000102043152},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.29820001125335693},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29429998993873596},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.2915000021457672},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C41426520","wikidata":"https://www.wikidata.org/wiki/Q1192065","display_name":"Point estimation","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.26269999146461487},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25870001316070557},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.02727","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02727","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":"doi:10.48550/arxiv.2604.02727","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02727","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":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.7939457297325134}],"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],"study":[1],"data-driven":[2],"computation":[3],"of":[4,36,79,95],"probabilistic":[5],"controlled":[6],"invariant":[7],"sets":[8],"(PCIS)":[9],"for":[10],"safety-critical":[11],"reinforcement":[12],"learning":[13],"under":[14],"unknown":[15],"dynamics.":[16],"Assuming":[17],"a":[18,33,47,68,76,91,116,120,127,140,145,157],"linear":[19],"MDP":[20],"model,":[21],"we":[22,114,132],"use":[23,133],"regularized":[24],"least":[25,108],"squares":[26],"and":[27,71,119,152],"self-normalized":[28],"confidence":[29,106],"bounds":[30],"to":[31,125],"construct":[32],"conservative":[34,77,92,136],"estimate":[35],"the":[37,41,57,80,86,96,134,154],"states":[38],"from":[39],"which":[40],"system":[42],"can":[43,72,99],"be":[44,73,100],"kept":[45],"inside":[46],"prescribed":[48],"safe":[49,60],"region":[50],"over":[51],"an":[52,103],"\\(N\\)-step":[53,81],"horizon,":[54],"together":[55],"with":[56,105,149],"corresponding":[58],"set-valued":[59],"action":[61],"map.":[62],"This":[63],"construction":[64],"is":[65],"obtained":[66],"through":[67],"backward":[69],"recursion":[70,98],"interpreted":[74],"as":[75,102,139],"approximation":[78,129,138],"safety":[82],"predecessor":[83],"operator.":[84],"When":[85],"associated":[87],"conservative-inclusion":[88],"event":[89],"holds,":[90],"fixed":[93],"point":[94],"approximate":[97],"certified":[101],"\\((N,\u03b5)\\)-PCIS":[104],"at":[107],"\\(\u03b7\\).":[109],"For":[110],"continuous":[111],"state":[112],"spaces,":[113],"introduce":[115],"lattice":[117],"abstraction":[118],"Lipschitz-based":[121],"discretization":[122],"error":[123],"bound":[124],"obtain":[126],"tractable":[128],"scheme.":[130],"Finally,":[131],"resulting":[135],"fixed-point":[137],"runtime":[141],"candidate":[142],"PCIS":[143],"in":[144],"practical":[146],"shielding":[147],"architecture":[148],"iterative":[150],"updates,":[151],"illustrate":[153],"approach":[155],"on":[156],"numerical":[158],"experiment.":[159]},"counts_by_year":[],"updated_date":"2026-04-07T06:06:30.997549","created_date":"2026-04-07T00:00:00"}