Accelerated Zeroth-order Algorithm for Stochastic Distributed Nonconvex Optimization

TL;DR

This paper introduces an accelerated zeroth-order distributed optimization algorithm with a primal-dual stochastic coordinate approach and 'powerball' method, achieving faster convergence for nonconvex problems with only zeroth-order information.

Contribution

It proposes a novel accelerated zeroth-order distributed primal-dual stochastic coordinate algorithm with 'powerball' method, providing theoretical convergence guarantees and improved empirical performance.

Findings

Achieves convergence rate of O(√p/√nT) for nonconvex functions.

Demonstrates faster convergence in numerical experiments.

Matches theoretical analysis with empirical results.

Abstract

This paper investigates how to accelerate the convergence of distributed optimization algorithms on nonconvex problems with zeroth-order information available only. We propose a zeroth-order (ZO) distributed primal-dual stochastic coordinates algorithm equipped with "powerball" method to accelerate. We prove that the proposed algorithm has a convergence rate of $\mathcal{O}(\sqrt{p}/\sqrt{nT})$ for general nonconvex cost functions. We consider solving the generation of adversarial examples from black-box DNNs problem to compare with the existing state-of-the-art centralized and distributed ZO algorithms. The numerical results demonstrate the faster convergence rate of the proposed algorithm and match the theoretical analysis.