{"id":"https://openalex.org/W7214957666","doi":"https://doi.org/10.48550/arxiv.2609.36030","title":"Preferent Compression Bounds Are Tight","display_name":"Preferent Compression Bounds Are Tight","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214957666","doi":"https://doi.org/10.48550/arxiv.2609.36030"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36030","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36030","pdf_url":"https://arxiv.org/pdf/2609.36030","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":null,"license_id":null,"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/2609.36030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064645708","display_name":"Dario Paccagnan","orcid":"https://orcid.org/0000-0002-8541-6966","observed_orcids":["https://orcid.org/0000-0002-8541-6966"]},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Paccagnan, Dario","raw_affiliation_strings":["Department of Computing , Imperial College London , London , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing , Imperial College London , London , UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005525683","display_name":"Marius A. Tirlea","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tirlea, Marius","raw_affiliation_strings":["Department of Computing , Imperial College London , London , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing , Imperial College London , London , UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I47508984"],"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/T12072","display_name":"Machine Learning and Algorithms","score":0.6791999936103821,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.6791999936103821,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.06400000303983688,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.023900000378489494,"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/sample-compression","display_name":"sample compression","score":0.9240000247955322},{"id":"https://openalex.org/keywords/stability","display_name":"stability","score":0.5080000162124634},{"id":"https://openalex.org/keywords/tightness-of-bounds","display_name":"tightness of bounds","score":0.703000009059906},{"id":"https://openalex.org/keywords/safety-certificates","display_name":"safety certificates","score":0.6299999952316284},{"id":"https://openalex.org/keywords/learning-control","display_name":"learning control","score":0.7080000042915344},{"id":"https://openalex.org/keywords/scenario-method","display_name":"scenario approach","score":0.7519999742507935},{"id":"https://openalex.org/keywords/order-statistics","display_name":"order statistics","score":0.6589999794960022},{"id":"https://openalex.org/keywords/uniform-distribution","display_name":"uniform distribution","score":0.6890000104904175}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6299999952316284},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.6111999750137329},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.5748000144958496},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5547999739646912},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41670000553131104},{"id":"https://openalex.org/C134121241","wikidata":"https://www.wikidata.org/wiki/Q899301","display_name":"Yield (engineering)","level":2,"score":0.40639999508857727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4043999910354614},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.38760000467300415},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.365200012922287},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3531999886035919},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35249999165534973},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.31360000371932983},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2976999878883362},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C81081738","wikidata":"https://www.wikidata.org/wiki/Q55542","display_name":"Lossless compression","level":3,"score":0.29190000891685486},{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2587999999523163},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25859999656677246},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25380000472068787},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36030","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36030","pdf_url":"https://arxiv.org/pdf/2609.36030","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.36030","doi":"https://doi.org/10.48550/arxiv.2609.36030","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36030","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36030","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36030","pdf_url":"https://arxiv.org/pdf/2609.36030","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6079119767","display_name":"COmpetition models and cross-Subsidies for equitable and green MObility - COSMO","funder_award_id":"EP/Y001001/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320314731","display_name":"UK Research and Innovation","ror":"https://ror.org/001aqnf71"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214957666.pdf","grobid_xml":"https://content.openalex.org/works/W7214957666.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7109219815"],"related_works":["https://openalex.org/W7221529960","https://openalex.org/W2962732488","https://openalex.org/W3151697588","https://openalex.org/W2136945987","https://openalex.org/W4403796893","https://openalex.org/W7162421992","https://openalex.org/W2181530505","https://openalex.org/W6987571401","https://openalex.org/W2018878471","https://openalex.org/W7133232773"],"abstract_inverted_index":{"The":[0],"lack":[1],"of":[2,15,138],"rigorous":[3],"safety":[4],"and":[5,68,90,115,134,146],"performance":[6],"certificates":[7],"remains":[8],"a":[9,25,40,131],"key":[10],"bottleneck":[11],"to":[12],"the":[13,50,64,93,112,120,123,126],"deployment":[14],"modern":[16],"learning-based":[17],"methods.":[18,71],"Sample":[19],"compression":[20],"has":[21,77],"recently":[22],"emerged":[23],"as":[24,47,61,63],"powerful":[26],"tool":[27],"for":[28,37,96],"deriving":[29],"such":[30],"certificates,":[31],"with":[32],"particularly":[33],"sharp":[34],"bounds":[35,55],"available":[36],"algorithms":[38],"satisfying":[39],"so-called":[41],"preference":[42],"property":[43],"--":[44],"also":[45,129],"known":[46],"stability":[48],"in":[49,122],"learning":[51],"theory":[52],"literature.":[53],"These":[54],"find":[56],"direct":[57],"application":[58],"across":[59],"domains":[60],"different":[62],"Scenario":[65],"Approach,":[66],"Pick-to-Learn,":[67],"Support":[69],"Vector":[70],"However,":[72],"whether":[73],"they":[74],"are":[75],"tight":[76],"remained":[78],"an":[79,107],"open":[80],"problem.":[81],"In":[82],"this":[83,87,104,139],"paper":[84],"we":[85,128],"resolve":[86],"question":[88],"affirmatively":[89],"show":[91],"that":[92,118],"state-of-the-art":[94],"bound":[95,121],"preferent":[97],"compressions":[98],"is":[99],"provably":[100],"tight.":[101],"We":[102],"establish":[103],"by":[105],"exhibiting":[106],"explicit":[108],"construction":[109],"based":[110],"on":[111],"uniform":[113],"distribution":[114],"order":[116],"statistics":[117],"attains":[119],"limit.":[124],"Along":[125],"way,":[127],"provide":[130],"considerably":[132],"shorter":[133],"more":[135],"accessible":[136],"proof":[137],"bound,":[140],"requiring":[141],"only":[142],"elementary":[143],"counting":[144],"arguments":[145],"no":[147],"infinite-dimensional":[148],"duality.":[149]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}