A Multi-Step Inertial ADMM Algorithm for Federated Learning

Federated learning has recently emerged as an important paradigm for large-scale distributed model training, which can be naturally formulated as a class of distributed learning problems. The alternating direction method of multipliers (ADMM) is a widely used approach for solving such problems. However, its practical performance is often hindered by significant communication overhead and system heterogeneity. In this paper, we propose a multi-step inertial ADMM algorithm, called MiFedADMM, for federated learning. The proposed method leverages multiple historical iterates on the server side to construct a higher-order extrapolation after each aggregation to accelerate the convergence behavior. Under mild assumptions, we establish convergence results for the single-step variant of the proposed method and derive an O(1/K) convergence rate. Numerical experiments on both synthetic and real-world datasets demonstrate the effectiveness and improved performance of the proposed method compared with existing approaches.