Distributed proximal gradient algorithm for non-smooth non-convex optimization over time-varying networks

TL;DR

This paper introduces a distributed proximal gradient algorithm for non-smooth, non-convex optimization over dynamic networks, ensuring convergence to critical points with proven rates and practical effectiveness.

Contribution

It proposes a novel distributed algorithm combining consensus and proximal steps for non-convex, non-smooth problems over time-varying networks, with convergence guarantees.

Findings

Achieves consensus among agents.

Converges to critical points at rate O(1/T).

Validated through numerical simulations.

Abstract

This note 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 different 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. Each agent updates local variable estimate by the multi-step consensus operator and the proximal operator. We prove that the generated local variables achieve consensus and converge to the set of critical points with convergence rate $O(1/T)$. Finally, we verify the efficacy of proposed algorithm by numerical simulations.