What question did this study set out to answer?

The research aims to address the nonconvex federated composite optimization problem with efficient algorithmic solutions.

February 8, 2026

Nonconvex Federated Composite Optimization With Random Reshuffling and Biased Compression

Key Points

The research aims to address the nonconvex federated composite optimization problem with efficient algorithmic solutions.
Proposed the FedRREF algorithm leveraging error feedback and random reshuffling techniques.
Focused on nonconvex loss functions with nonsmooth regularizers.
Analyzed the algorithm's performance through numerical experiments.
FedRREF achieves a convergence rate of $A9(1/3A3T)$ with T as the number of communication rounds.
Demonstrated reduced computation and communication costs compared to existing methods.

Abstract

This article focuses on nonconvex federated composite optimization (FCO) problem, where the loss function is nonconvex and contains a nonsmooth regularizer. To resolve this problem, we propose FedRREF, a novel federated learning algorithm that integrates error feedback (EF) with the efficient random reshuffling (RR) technique, resulting in lower computation and communication costs. To the best of our knowledge, FedRREF is the first algorithm to consider RR and biased compression simultaneously in federated learning, especially in nonsmooth and nonconvex settings, and it is shown to have a O (1/T) convergence rate, where T is the number of communication rounds. Finally, the numerical experiments illustrate the validity of the proposed algorithm.

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