Near-Optimal Decentralized Stochastic Nonconvex Optimization with Heavy-Tailed Noise

TL;DR

This paper introduces a decentralized normalized stochastic gradient descent method that effectively handles heavy-tailed noise in nonconvex optimization, achieving near-optimal sample and communication complexities.

Contribution

It proposes a novel decentralized optimization algorithm robust to heavy-tailed noise, with theoretical guarantees and empirical validation.

Findings

Achieves approximate stationary points with optimal sample complexity.

Attains near-optimal communication complexity.

Demonstrates practical superiority through empirical studies.

Abstract

This paper studies decentralized stochastic nonconvex optimization problem over row-stochastic networks. We consider the heavy-tailed gradient noise which is empirically observed in many popular real-world applications. Specifically, we propose a decentralized normalized stochastic gradient descent with Pull-Diag gradient tracking, which achieves approximate stationary points with the optimal sample complexity and the near-optimal communication complexity. We further follow our framework to study the setting of undirected networks, also achieving the nearly tight upper complexity bounds. Moreover, we conduct empirical studies to show the practical superiority of the proposed methods.