Distributed Stochastic Optimization for Non-Smooth and Weakly Convex Problems under Heavy-Tailed Noise

TL;DR

This paper introduces a distributed stochastic optimization algorithm designed for non-smooth, weakly convex problems affected by heavy-tailed noise, addressing a gap in existing methods that assume bounded variance.

Contribution

It proposes a novel clipping-based algorithm that handles heavy-tailed noise in non-smooth, weakly convex settings, with proven convergence guarantees.

Findings

Algorithm effectively handles heavy-tailed noise.

Convergence conditions are established.

Numerical experiments demonstrate improved performance.

Abstract

In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to practical scenarios in many tasks. Under heavy-tailed noise, traditional optimization methods, such as stochastic gradient descent, may have poor performance and even diverge. Thus, it is of great importance to study distributed stochastic optimization algorithms applicable to the heavy-tailed noise scenario. However, most of the existing distributed algorithms under heavy-tailed noise are developed for convex and smooth problems, which limits their applications. This paper proposes a clipping-based distributed stochastic algorithm under heavy-tailed noise that is suitable for non-smooth and weakly convex problems. The convergence of the proposed algorithm is proven, and the conditions on the parameters are given. A numerical experiment is conducted to demonstrate the effectiveness of the proposed algorithm.