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

Shuyu Cheng, Guoqiang Wu, Jun Zhu

Keywords: zeroth-order optimization, gradient-free optimization, evolutionary strategies, convex optimization, randomized methods

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.

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TL;DR: We conduct convergence analysis on frameworks of ZO algorithms including existing prior-guided random gradient-free methods and a new prior-guided accelerated random search method.

Code: https://github.com/csy530216/pg-zoo

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2107.10110/code)