Zeroth-Order Stochastic Variance Reduction for Nonconvex Optimization
It addresses the need for faster and more efficient zeroth-order optimization methods, which is crucial for applications where gradient information is unavailable, but the work is incremental as it builds on existing variance reduction techniques.
This paper tackles the problem of zeroth-order (gradient-free) optimization by proposing ZO-SVRG, a novel variance-reduced algorithm, and shows it outperforms other state-of-the-art methods in applications like black-box chemical material classification and adversarial example generation, achieving the best known convergence rate in iterations.
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.