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This research addresses critical distributional shifts in federated learning by constructing robust ambiguity sets that account for both cross-client mixture uncertainty and finite-sample estimation errors. The proposed algorithm offers a client-wise separable reformulation with proven convergence under milder conditions, providing high-probability out-of-sample performance guarantees. Such theoretical advances are essential for deploying reliable AI models across heterogeneous data environments where traditional assumptions often fail.
Distributionally Robust Federated Learning with Multi-Source Data
arXiv:2609.20501v1 Announce Type: new Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2609.20501 [cs.LG]
(or arXiv:2609.20501v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.20501 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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