Optimal Uncertainty Budget Allocation for Robust Federated Learning under Byzantine Attacks

Optimal Uncertainty Budget Allocation for Robust Federated Learning under Byzantine Attacks | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Optimal Uncertainty Budget Allocation for Robust Federated Learning under Byzantine Attacks Weiwei Lian, Jun Tao, Xinjun Mei, Yu Fang, Zhou Shen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7406272/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Federated learning (FL) has revolutionized the development of machine learning models by enabling decentralized training while safeguarding user privacy. However, the presence of Byzantine adversaries introduces significant vulnerabilities, as malicious clients can disrupt the learning process by providing misleading updates. This paper addresses the critical challenge of allocating an uncertainty budget across heterogeneous clients to enhance the robustness of federated learning systems against such adversarial attacks. We introduce the Uncertainty Budget Allocation Problem (UBAP), formulating it as a mixed-integer nonlinear program (MINLP) aimed at optimizing resource distribution for improved model convergence and stability. Our framework not only rethinks traditional assumptions about client contributions but also presents a novel mathematical analysis underlying the relationship between uncertainty allocation and adversarial strength. Extensive empirical evaluations on standard benchmarks demonstrate substantial improvements in model performance and resistance to attacks, showcasing the practical efficacy of our approach. Through this work, we underscore the importance of optimal uncertainty budget allocation to foster resilience in federated learning systems, paving the way for further innovations in this domain and enhancing the security of decentralized AI applications. robust optimization federated learning Byzantine attacks uncertainty quantification mixed-integer programming adversarial robustness Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7406272","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":505549206,"identity":"bf3c504a-4152-4752-84f2-947adda072a4","order_by":0,"name":"Weiwei Lian","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Weiwei","middleName":"","lastName":"Lian","suffix":""},{"id":505549207,"identity":"21dd762a-2f4e-4be4-99e2-9ee8b4beaa8d","order_by":1,"name":"Jun Tao","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Tao","suffix":""},{"id":505549208,"identity":"8b57fa18-6339-4a7d-954d-16eb86f122ed","order_by":2,"name":"Xinjun Mei","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Xinjun","middleName":"","lastName":"Mei","suffix":""},{"id":505549209,"identity":"c9b95dfb-b593-4e18-89c8-d5f0b0eafeac","order_by":3,"name":"Yu Fang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yu","middleName":"","lastName":"Fang","suffix":""},{"id":505549210,"identity":"a2fbfcff-a26e-4a53-ac74-268e65a6b6c3","order_by":4,"name":"Zhou Shen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFElEQVRIiWNgGAWjYDACCSBmbEASMGAH8QwsSNHCcwBESpCiRSIBJo4dyM9uPvbw5w6bxAbpw4c/fKi5J28u+fzqhh8FEgz87d0J2LQY3DmWbiB5Ji2xgS8tTXLGsWLDnbNzym72AB0mcebsBqxaJHLMJAzbDic28PCYMfOwJSQY3M5Ju8ED1GIgkYtVi/yM/G8SiWAt/J8///kH1HLzTNrNP3i0MNzIYZM4CLGFQZqxDajlBvux2/hsMbiRZibZ2JZm3MbDZibZ25dguOFMDtttGQMJHlx+kZ+R/EzyZ5uNbD8P8+MPP74lyBscP/7s5ps/NnL87b3YHQYDbAgmjwGYxKscDbA/IEX1KBgFo2AUDH8AAA8DYpsNUdNBAAAAAElFTkSuQmCC","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Zhou","middleName":"","lastName":"Shen","suffix":""}],"badges":[],"createdAt":"2025-08-19 08:33:59","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7406272/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7406272/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90005587,"identity":"f8a89f65-8785-464c-86a1-454a10962bb6","added_by":"auto","created_at":"2025-08-27 09:35:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":245369,"visible":true,"origin":"","legend":"","description":"","filename":"paper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7406272/v1_covered_11be1630-76f3-487f-a498-e94c5f474d6b.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eOptimal Uncertainty Budget Allocation for Robust Federated Learning under Byzantine Attacks\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"robust optimization, federated learning, Byzantine attacks, uncertainty quantification, mixed-integer programming, adversarial robustness","lastPublishedDoi":"10.21203/rs.3.rs-7406272/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7406272/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFederated learning (FL) has revolutionized the development of machine learning models by enabling decentralized training while safeguarding user privacy. 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