Learning to Optimize with Distributional Shift Constraints: A Novel Framework for Safe Domain Adaptation in Machine Learning

Learning to Optimize with Distributional Shift Constraints: A Novel Framework for Safe Domain Adaptation in Machine Learning | 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 Learning to Optimize with Distributional Shift Constraints: A Novel Framework for Safe Domain Adaptation in Machine Learning Li Wei, Zhangzhi Ying, Chenchen Feng, Liu Jun, Ziwang Qian, Zhao Li, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7250445/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 Domain adaptation remains a significant challenge in machine learning, particularly in real-world applications where distributional shifts between training and testing domains can lead to drastic performance degradation. This paper presents a novel framework that integrates explicit constraints for worst-case distributional shifts into the empirical risk minimization process, employing integral probability metrics. By characterizing the optimization problem through optimal transport theory, we derive a mathematically rigorous solution that ensures robustness and safety in the adaptation process. Our approach is scrutinized through comprehensive theoretical analysis, establishing guarantees for the performance of adapted models. Extensive experimental evaluations on synthetic and real-world datasets demonstrate the framework's efficacy, revealing substantial improvements over existing domain adaptation methods in scenarios with severe distributional shifts. We underscore the importance of robust domain adaptation methodologies in fostering trust in AI systems deployed across sensitive domains. The proposed framework not only enhances the reliability of machine learning models but also paves the way for future research addressing the complexities of distributional uncertainty. Distributional Shift Safe Domain Adaptation Optimal Transport Constrained Optimization Integral Probability Metrics Empirical Risk Minimization 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-7250445","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":500894124,"identity":"4ef58a56-4bc0-4b20-a6f0-c0c5505c5468","order_by":0,"name":"Li Wei","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Li","middleName":"","lastName":"Wei","suffix":""},{"id":500894125,"identity":"ea2726c0-4b6b-4019-8628-b8a05e72d944","order_by":1,"name":"Zhangzhi 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