On the Convergence of Prior-Guided Zeroth-Order Optimization Algorithms

TL;DR

This paper analyzes the convergence of prior-guided zeroth-order optimization algorithms, introduces an accelerated method, and validates theoretical findings through experiments on benchmarks and adversarial attacks.

Contribution

It provides the first convergence guarantees for prior-guided ZO algorithms and proposes an accelerated method incorporating prior information.

Findings

Convergence guarantee for prior-guided random gradient-free algorithms.

Introduction of an accelerated random search algorithm with proven convergence.

Experimental validation on benchmarks and adversarial attack tasks.

Abstract

Zeroth-order (ZO) optimization is widely used to handle challenging tasks, such as query-based black-box adversarial attacks and reinforcement learning. Various attempts have been made to integrate prior information into the gradient estimation procedure based on finite differences, with promising empirical results. However, their convergence properties are not well understood. This paper makes an attempt to fill up this gap by analyzing the convergence of prior-guided ZO algorithms under a greedy descent framework with various gradient estimators. We provide a convergence guarantee for the prior-guided random gradient-free (PRGF) algorithms. Moreover, to further accelerate over greedy descent methods, we present a new accelerated random search (ARS) algorithm that incorporates prior information, together with a convergence analysis. Finally, our theoretical results are confirmed by experiments on several numerical benchmarks as well as adversarial attacks.