FDR-SVM: A Federated Distributionally Robust Support Vector Machine via a Mixture of Wasserstein Balls Ambiguity Set

Michael Ibrahim, Heraldo Rozas, Nagi Gebraeel, Weijun Xie

Keywords: distributionally robust optimization, federated learning, classification, data uncertainty, support vector machine

TL;DR: We propose an FDR-SVM--a classifier that is distributionally robust to uncertainty in training data features and labels, and can be trained via our proposed algorithms in a federated fashion thanks to our novel MoWB ambiguity set.

Abstract: We study a federated classification problem over a network of multiple clients and a central server, in which each client’s local data remains private and is subject to uncertainty in both the features and labels. To address these uncertainties, we develop a novel Federated Distributionally Robust Support Vector Machine (FDR-SVM), robustifying the classification boundary against perturbations in local data distributions. Specifically, the data at each client is governed by a unique true distribution that is unknown. To handle this heterogeneity, we develop a novel Mixture of Wasserstein Balls (MoWB) ambiguity set, naturally extending the classical Wasserstein ball to the federated setting. We then establish theoretical guarantees for our proposed MoWB, deriving an out-of-sample performance bound and showing that its design preserves the separability of the FDR-SVM optimization problem. Next, we rigorously derive two algorithms that solve the FDR-SVM problem and analyze their convergence behavior as well as their worst-case time complexity. We evaluate our algorithms on industrial data and various UCI datasets, whereby we demonstrate that they frequently outperform existing state-of-the-art approaches.

Code Link: https://github.com/mibrahim41/FDR-SVM https://youtu.be/NWyJGSVlxyQ

Readers: auai.org/UAI/2025/Conference, auai.org/UAI/2025/Conference/Area_Chairs, auai.org/UAI/2025/Conference/Reviewers, auai.org/UAI/2025/Conference/Submission573/Authors, auai.org/UAI/2025/Conference/Submission573/Reproducibility_Reviewers

Submission Number: 573