# Distributionally Robust Federated Learning with Multi-Source Data

arXiv: https://arxiv.org/abs/2609.20501 · HTML: https://mlsanity.com/paper/2609.20501/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Near-Optimal Algorithms for Group Distributionally Robust Optimization and Beyond](https://mlsanity.com/paper/2212.13669/) (2022)
- [Efficient Algorithms for Empirical Group Distributionally Robust Optimization and Beyond](https://mlsanity.com/paper/2403.03562/) (2024)
- [On the Generalization of Wasserstein Robust Federated Learning](https://mlsanity.com/paper/2206.01432/) (2022)
- [Cooperative data-driven distributionally robust optimization](https://mlsanity.com/paper/1711.04839/) (2017)
- [High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems](https://mlsanity.com/paper/2102.01142/) (2021)
- [Group Distributionally Robust Machine Learning under Group Level Distributional Uncertainty](https://mlsanity.com/paper/2509.08942/) (2025)
- [FDR-SVM: A Federated Distributionally Robust Support Vector Machine via a Mixture of Wasserstein Balls Ambiguity Set](https://mlsanity.com/paper/2410.03877/) (2024)
- [Distributionally Robust Federated Learning with Outlier Resilience](https://mlsanity.com/paper/2509.24462/) (2025)

## Abstract (arXiv)

Federated learning trains a shared model from private client data. In practice, data-generating distributions may differ, and the true mixture across clients is often unknown, making the underlying group distribution difficult to specify. Existing approaches address cross-client mixture uncertainty by optimizing against the worst-case mixture, yet assume accurate client-wise distribution estimates. However, these estimates can be unreliable when based on finite samples. To handle both cross-client mixture uncertainty and within-client distributional ambiguity, we construct a global ambiguity set as the union of admissible mixtures of local ambiguity sets. The construction allows client-specific ambiguity radii and admits a client-wise separable reformulation. Leveraging this structure, we establish a high-probability out-of-sample performance guarantee. We further develop a federated algorithm for a penalty-based reformulation and prove its convergence under milder regularity conditions. Simulations validate the algorithm's effectiveness.