Mitigating Data Heterogeneity Effect in Client-Reshuffling-Based Federated Learning

Data heterogeneity and low client participation are two key challenges in federated learning (FL). Client-reshuffling-based FL methods were recently introduced to improve participation efficiency by visiting each client once per meta-epoch; however, the resulting \textit{without-replacement} sampling induces inter-round dependence and conditional bias. As a consequence, existing client-reshuffling methods can still suffer from the data heterogeneity challenge due to this dependence. To bridge this gap, we propose \textbf{FedCDR}, a client-reshuffling FL algorithm built on Douglas–Rachford splitting. FedCDR supports \textit{inexact} local proximal updates via iterative solvers, enabling a practical communication–computation trade-off. For smooth nonconvex objectives, FedCDR with inexact local solvers attains a state-of-the-art $O(\epsilon^{-1})$ communication complexity to reach an $\epsilon$-approximate stationary point (i.e., $\mathbb{E}\|\nabla f(\tilde{x})\|^2 \le \epsilon)$, with the leading constant that is \textbf{independent of data heterogeneity} (i.e., it does not scale with common measures of heterogeneity). Technically, our analysis operates at the meta-epoch level: we control the deviation between reshuffled and full-client updates, construct a tailored potential function with provable descent, and sum over each meta-epoch to eliminate reshuffling-induced dependence. Experiments on synthetic tasks and benchmark datasets under heterogeneous partitions, including a 10,000-client setting, demonstrate consistent improvements over strong baselines and their client reshuffling variants.