Abstract: To address the core challenges of limited communication bandwidth, insufficient computational resources, and data heterogeneity in federated learning, this paper proposes a variance-reduced federated symmetric alternating direction method of multipliers, termed FedSADMM-VR. Built upon the Symmetric ADMM framework, the proposed method introduces a periodic communication strategy to reduce communication overhead, and employs variance-reduced stochastic gradients to inexactly solve linearized subproblems, thereby effectively lowering both the local computational complexity and the overall communication cost. Furthermore, the algorithm performs symmetric dual variable updates during the local update process, which mitigates the information bias induced by dual variable staleness and enhances the stability of the model under non-independent and identically distributed data. Theoretical analysis establishes that, in the non-convex setting, the algorithm achieves a sublinear convergence rate without requiring the bounded gradient dissimilarity assumption. Experimental results on synthetic data and the a9a, phishing, and FEMNIST datasets demonstrate that FedSADMM-VR can maintain effective test accuracy while reducing the number of communication rounds, and exhibits relatively stable convergence behavior under non-independent and identically distributed data settings.

Key words: federated learning, symmetric alternating direction method of multipliers, variance reduction, convergence analysis, image classification