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

arXiv: https://arxiv.org/abs/2410.03877 · HTML: https://mlsanity.com/paper/2410.03877/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 62 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 24 of 24)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Distributionally Robust Federated Averaging](https://mlsanity.com/paper/2102.12660/) (2021)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Outlier-Robust Wasserstein DRO](https://mlsanity.com/paper/2311.05573/) (2023)
- [Parallel Multi-Block ADMM with o(1/k) Convergence](https://mlsanity.com/paper/1312.3040/) (2013)
- [Compositional federated learning: Applications in distributionally robust averaging and meta learning](https://mlsanity.com/paper/2106.11264/) (2021)
- [Communication-Efficient Distributionally Robust Decentralized Learning](https://mlsanity.com/paper/2205.15614/) (2022)
- [Cooperative data-driven distributionally robust optimization](https://mlsanity.com/paper/1711.04839/) (2017)
- [Wasserstein Logistic Regression with Mixed Features](https://mlsanity.com/paper/2205.13501/) (2022)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [DRFLM: Distributionally Robust Federated Learning with Inter-client Noise via Local Mixup](https://mlsanity.com/paper/2204.07742/) (2022)
- [Modeling the Q-Diversity in a Min-max Play Game for Robust Optimization](https://mlsanity.com/paper/2305.12123/) (2023)
- [FedDRO: Federated Compositional Optimization for Distributionally Robust Learning](https://mlsanity.com/paper/2311.12652/) (2023)

## Built on by (most cited first, 1 of 1)

- [Distributionally Robust Federated Learning with Multi-Source Data](https://mlsanity.com/paper/2609.20501/) (2026)

## Abstract (arXiv)

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.