Zeroth-Order Stochastic Variance Reduction for Nonconvex Optimization

TL;DR

This paper introduces ZO-SVRG, a variance reduced zeroth-order optimization algorithm with theoretical analysis and practical applications, demonstrating improved convergence and efficiency in black-box problems.

Contribution

It presents a novel variance reduced zeroth-order algorithm, ZO-SVRG, with theoretical insights and accelerated variants, advancing zeroth-order optimization methods.

Findings

ZO-SVRG outperforms existing ZO algorithms in convergence speed

Accelerated ZO-SVRG achieves the best known iteration rate for ZO stochastic optimization

Experimental results validate the effectiveness of the proposed methods in real-world applications

Abstract

As application demands for zeroth-order (gradient-free) optimization accelerate, the need for variance reduced and faster converging approaches is also intensifying. This paper addresses these challenges by presenting: a) a comprehensive theoretical analysis of variance reduced zeroth-order (ZO) optimization, b) a novel variance reduced ZO algorithm, called ZO-SVRG, and c) an experimental evaluation of our approach in the context of two compelling applications, black-box chemical material classification and generation of adversarial examples from black-box deep neural network models. Our theoretical analysis uncovers an essential difficulty in the analysis of ZO-SVRG: the unbiased assumption on gradient estimates no longer holds. We prove that compared to its first-order counterpart, ZO-SVRG with a two-point random gradient estimator could suffer an additional error of order $O(1/b)$, where $b$ is the mini-batch size. To mitigate this error, we propose two accelerated versions of ZO-SVRG utilizing variance reduced gradient estimators, which achieve the best rate known for ZO stochastic optimization (in terms of iterations). Our extensive experimental results show that our approaches outperform other state-of-the-art ZO algorithms, and strike a balance between the convergence rate and the function query complexity.