Nonconvex Federated Composite Optimization With Random Reshuffling and Biased Compression

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 $\mathcal {O}(1/\sqrt {T})$ convergence rate, where $T$ is the number of communication rounds. Finally, the numerical experiments illustrate the validity of the proposed algorithm.