Fast automatic step size selection for zeroth-order nonconvex stochastic optimization

Abstract

The efficacy and simplicity of using only function evaluations in zeroth-order stochastic optimization (ZOSO) makes it achieve great attention in solving large scale learning tasks. However, the question of how to choose an appropriate step size sequence timely for ZOSO has been less researched. To fill this defect, this paper provides a fast automatic step size selection approach by using an improved Barzilai-Borwein (IBB) technique with the zeroth-order (ZO) gradient estimator for ZOSO. In detail, this work shows the efficacy of the IBB technique by applying it into the advanced ZOSO method, i.e., zeroth-order stochastic variance reduced gradient (ZO-SVRG) method, which leads to a method: ZO-SVRG-IBB. We theoretically analyze the convergence of the ZO-SVRG-IBB method under the random gradient estimator and the coordinate-wise gradient estimator settings, respectively, and show that the convergence rate of ZO-SVRG-IBB matches the best-known convergence rate of advanced ZOSO methods on nonconvex functions. We further show that the query complexity of ZO-SVRG-IBB is comparable to advanced ZOSO methods. Extensive numerical experiments performed on different datasets show that the proposed method outperforms or matches state-of-the-art ZOSO methods.