Two-timescale EXTRA for Distributed Smooth Non-convex Optimization

Abstract

In this paper, we study distributed optimization with smooth non-convex local objectives. We propose a novel variant of the well-known EXact firsT-ordeR Algorithm (EXTRA), called Two-timescale EXTRA, by introducing two distinct step-sizes. Leveraging the two-timescale strategy, we construct a Lyapunov function and establish the sub-linear convergence of Two-timescale EXTRA to a consensual first-order stationary point. Additionally, we introduce an off-line sequential method for algorithm parameter selection, and the numerical results support the theoretical guarantees.