Compressed Momentum-based Single-Point Zeroth-Order Algorithm for Stochastic Distributed Nonconvex Optimization

TL;DR

This paper introduces a novel compressed momentum-based zeroth-order algorithm for stochastic distributed nonconvex optimization, reducing communication costs and functioning without explicit gradient information.

Contribution

It develops a new algorithm that combines compression, momentum, and zeroth-order methods for efficient distributed nonconvex optimization.

Findings

Proves convergence to the exact solution with diminishing step sizes.

Achieves sublinear convergence to a neighborhood of stationary points with fixed step sizes.

Numerical experiments demonstrate improved communication efficiency.

Abstract

This paper studies a compressed momentum-based single-point zeroth-order algorithm for stochastic distributed nonconvex optimization, aiming to alleviate communication overhead and address the unavailability of explicit gradient information. In the developed framework, each agent has access only to stochastic zeroth-order information of its local objective function, performs local stochastic updates with momentum, and exchanges compressed updates with its neighbors. We theoretically prove that the proposed algorithm can achieve the exact solution with diminishing step sizes and can achieve a sublinear convergence rate towards a neighborhood of the stationary point with fixed step sizes. Numerical experiments validate the effectiveness and communication efficiency of the proposed algorithm.