Distributed stochastic proximal algorithm with random reshuffling for non-smooth finite-sum optimization

TL;DR

This paper introduces a distributed stochastic proximal-gradient algorithm with random reshuffling for non-smooth finite-sum optimization in multi-agent networks, achieving consensus and convergence with proven rates.

Contribution

It develops a novel distributed algorithm that handles non-smooth optimization with convergence guarantees over time-varying networks.

Findings

Achieves consensus among agents in expectation.

Converges to a neighborhood of the optimal solution at rate O(1/T + 1/√T).

Simulation results verify the theoretical convergence performance.

Abstract

The non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying multi-agent networks. The objective function is a sum of differentiable convex functions and non-smooth regularization. Each agent in the network updates local variables with a constant step-size by local information and cooperates to seek an optimal solution. We prove that local variable estimates generated by the proposed algorithm achieve consensus and are attracted to a neighborhood of the optimal solution in expectation with an $\mathcal{O}(\frac{1}{T}+\frac{1}{\sqrt{T}})$ convergence rate, where $T$ is the total number of iterations. Finally, some comparative simulations are provided to verify the convergence performance of the proposed algorithm.