{"id":"https://openalex.org/W7134833658","doi":"https://doi.org/10.48550/arxiv.2603.08558","title":"Impact of Connectivity on Laplacian Representations in Reinforcement Learning","display_name":"Impact of Connectivity on Laplacian Representations in Reinforcement Learning","publication_year":2026,"publication_date":"2026-03-09","ids":{"openalex":"https://openalex.org/W7134833658","doi":"https://doi.org/10.48550/arxiv.2603.08558"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.08558","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":"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/A5128663409","display_name":"Tommaso Giorgi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Giorgi, Tommaso","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044098126","display_name":"Pierriccardo Olivieri","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olivieri, Pierriccardo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128660911","display_name":"Keyue Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Keyue","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071335453","display_name":"Laura Toni","orcid":"https://orcid.org/0000-0002-8441-8791"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Toni, Laura","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015303026","display_name":"Matteo Papini","orcid":"https://orcid.org/0000-0002-3807-3171"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Papini, Matteo","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5128663409"],"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":0.9333999752998352,"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":0.9333999752998352,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.00989999994635582,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.00989999994635582,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6256999969482422},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6039000153541565},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.5965999960899353},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.589900016784668},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.5393999814987183},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4494999945163727},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.4180000126361847},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.38350000977516174},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.3578999936580658}],"concepts":[{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6256999969482422},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6039000153541565},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5965999960899353},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.589900016784668},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5393999814987183},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5214999914169312},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4494999945163727},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4180000126361847},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38350000977516174},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.3578999936580658},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3492000102996826},{"id":"https://openalex.org/C196340769","wikidata":"https://www.wikidata.org/wiki/Q7698910","display_name":"Temporal difference learning","level":3,"score":0.34860000014305115},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3382999897003174},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3361000120639801},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3255999982357025},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3239000141620636},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3188999891281128},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3091000020503998},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.29739999771118164},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2971000075340271},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.08558","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.2603.08558","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08558","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2603.08558","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":[{"score":0.7866935729980469,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Learning":[0],"compact":[1],"state":[2,35,53],"representations":[3,36],"in":[4,18,108],"Markov":[5],"Decision":[6],"Processes":[7],"(MDPs)":[8],"has":[9],"proven":[10],"crucial":[11],"for":[12,144,169],"addressing":[13],"the":[14,31,41,46,52,58,78,87,98,102,105,109,113,118,122,133,141,145,164,177,180],"curse":[15],"of":[16,40,81,101,112,140,157,179],"dimensionality":[17],"large-scale":[19],"reinforcement":[20],"learning":[21,135],"(RL)":[22],"problems.":[23],"Existing":[24],"principled":[25],"approaches":[26],"leverage":[27],"structural":[28],"priors":[29],"on":[30,77,176,192],"MDP":[32],"by":[33,121],"constructing":[34],"as":[37],"linear":[38,82],"combinations":[39],"state-graph":[42],"Laplacian":[43,142],"eigenvectors.":[44],"When":[45],"transition":[47,182],"graph":[48,59],"is":[49,55],"unknown":[50],"or":[51],"space":[54],"prohibitively":[56],"large,":[57],"spectral":[60,89],"features":[61],"can":[62],"be":[63],"estimated":[64],"directly":[65],"via":[66],"sample":[67],"trajectories.":[68],"In":[69],"this":[70,94],"work,":[71],"we":[72,159],"prove":[73],"an":[74,128],"upper":[75],"bound":[76,117],"approximation":[79,85,106],"error":[80,95,119,130],"value":[83],"function":[84],"under":[86],"learned":[88],"features.":[90],"We":[91,115,184],"show":[92,160],"how":[93],"scales":[96],"with":[97,189],"algebraic":[99],"connectivity":[100],"state-graph,":[103],"grounding":[104],"quality":[107],"topological":[110],"structure":[111],"MDP.":[114],"further":[116],"introduced":[120],"eigenvector":[123],"estimation":[124],"itself,":[125],"leading":[126],"to":[127,150],"end-to-end":[129],"decomposition":[131],"across":[132],"representation":[134],"pipeline.":[136],"Additionally,":[137],"our":[138,186],"expression":[139],"operator":[143],"RL":[146],"setting,":[147],"although":[148],"equivalent":[149],"existing":[151],"ones,":[152],"prevents":[153],"some":[154,161],"common":[155],"misunderstandings,":[156],"which":[158],"examples":[162],"from":[163],"literature.":[165],"Our":[166],"results":[167],"hold":[168],"general":[170],"(non-uniform)":[171],"policies":[172],"without":[173],"any":[174],"assumptions":[175],"symmetry":[178],"induced":[181],"kernel.":[183],"validate":[185],"theoretical":[187],"findings":[188],"numerical":[190],"simulations":[191],"gridworld":[193],"environments.":[194]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-03-11T00:00:00"}