{"id":"https://openalex.org/W7128066360","doi":"https://doi.org/10.48550/arxiv.2602.03899","title":"Byzantine Machine Learning: MultiKrum and an optimal notion of robustness","display_name":"Byzantine Machine Learning: MultiKrum and an optimal notion of robustness","publication_year":2026,"publication_date":"2026-02-03","ids":{"openalex":"https://openalex.org/W7128066360","doi":"https://doi.org/10.48550/arxiv.2602.03899"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.03899","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":null,"license_id":null,"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/A5081490349","display_name":"Gilles Bareilles","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bareilles, Gilles","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114331453","display_name":"Wassim Bouaziz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bouaziz, Wassim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015119381","display_name":"Julien Fageot","orcid":"https://orcid.org/0000-0002-2122-2580"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fageot, Julien","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125158314","display_name":"El-Mahdi El-Mhamdi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"El-Mhamdi, El-Mahdi","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":10.3239,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.96181782,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.5723000168800354,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.5723000168800354,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.15279999375343323,"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/T10883","display_name":"Ethics and Social Impacts of AI","score":0.05249999836087227,"subfield":{"id":"https://openalex.org/subfields/3311","display_name":"Safety Research"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.8446999788284302},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6291999816894531},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.2662999927997589},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.24699999392032623}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.8446999788284302},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6291999816894531},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.576200008392334},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.424699991941452},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4142000079154968},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38190001249313354},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3653999865055084},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.24699999392032623},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23090000450611115}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.03899","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.03899","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.03899","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":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.03899","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Aggregation":[0],"rules":[1],"are":[2,22,167],"the":[3,11,16,28,83,104,114,120,155,186,189],"cornerstone":[4],"of":[5,13,30,32,57,108,116,122,133,188],"distributed":[6],"(or":[7],"federated)":[8],"learning":[9],"in":[10,62,119,124,174],"presence":[12,121],"adversaries,":[14],"under":[15],"so-called":[17],"Byzantine":[18],"threat":[19],"model.":[20],"They":[21],"also":[23,152],"interesting":[24],"mathematical":[25],"objects":[26],"from":[27],"point":[29],"view":[31],"robust":[33,90],"mean":[34,117],"estimation.":[35],"The":[36],"Krum":[37],"aggregation":[38,91,110],"rule":[39],"has":[40],"been":[41],"extensively":[42],"studied,":[43],"and":[44,49,93,140,172],"endowed":[45],"with":[46,129],"formal":[47],"robustness":[48,96,146,160],"convergence":[50],"guarantees.":[51],"Yet,":[52],"MultiKrum,":[53],"a":[54,89,125,141,149],"natural":[55],"extension":[56],"Krum,":[58],"is":[59,88],"often":[60],"preferred":[61],"practice":[63],"for":[64],"its":[65,95],"superior":[66],"empirical":[67],"performance,":[68],"even":[69],"though":[70],"no":[71],"theoretical":[72],"guarantees":[73],"were":[74],"available":[75],"until":[76],"now.":[77],"In":[78],"this":[79,179],"work,":[80],"we":[81,101,151],"provide":[82],"first":[84],"proof":[85],"that":[86,164],"MultiKrum":[87],"rule,":[92,111],"bound":[94,143],"coefficient.":[97,147,161],"To":[98],"do":[99],"so,":[100],"introduce":[102],"$\u03ba^\\star$,":[103],"optimal":[105],"*robustness":[106],"coefficient*":[107],"an":[109,138,182],"which":[112],"quantifies":[113],"accuracy":[115],"estimation":[118],"adversaries":[123],"tighter":[126],"manner":[127],"compared":[128],"previously":[130],"adopted":[131],"notions":[132],"robustness.":[134],"We":[135,162,177],"then":[136],"construct":[137],"upper":[139],"lower":[142,190],"on":[144,154,158,185],"MultiKrum's":[145,165],"As":[148],"by-product,":[150],"improve":[153],"best-known":[156],"bounds":[157,166],"Krum's":[159],"show":[163],"never":[168],"worse":[169],"than":[170],"Krum's,":[171],"better":[173],"realistic":[175],"regimes.":[176],"illustrate":[178],"analysis":[180],"by":[181],"experimental":[183],"investigation":[184],"quality":[187],"bound.":[191]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2026-02-07T00:00:00"}
