Distributed Proximal Gradient Algorithm for Nonconvex Optimization Over Time-Varying Networks

Abstract

This paper studies the distributed non-convex optimization problem with non-smooth regularization, which has wide applications in decentralized learning, estimation and control. The objective function is the sum of local objective functions, which consist of differentiable (possibly non-convex) cost functions and non-smooth convex functions. This paper presents a distributed proximal gradient algorithm for the non-smooth non-convex optimization problem. Over time-varying multi-agent networks, the proposed algorithm updates local variable estimates with a constant step-size at the cost of multiple consensus steps, where the number of communication rounds increases over time. We prove that the generated local variables achieve consensus and converge to the set of critical points. Finally, we verify the efficiency of the proposed algorithm by numerical simulations.