Accelerated Stochastic Gradient-free and Projection-free Methods

Code

• github.com/TLMichael/Acc-SZOFW
  OfficialIn paperpytorch★ 5

Abstract

In the paper, we propose a class of accelerated stochastic gradient-free and projection-free (a.k.a., zeroth-order Frank-Wolfe) methods to solve the constrained stochastic and finite-sum nonconvex optimization. Specifically, we propose an accelerated stochastic zeroth-order Frank-Wolfe (Acc-SZOFW) method based on the variance reduced technique of SPIDER/SpiderBoost and a novel momentum accelerated technique. Moreover, under some mild conditions, we prove that the Acc-SZOFW has the function query complexity of O(dn^-2) for finding an -stationary point in the finite-sum problem, which improves the exiting best result by a factor of O(n^-2), and has the function query complexity of O(d^-3) in the stochastic problem, which improves the exiting best result by a factor of O(^-1). To relax the large batches required in the Acc-SZOFW, we further propose a novel accelerated stochastic zeroth-order Frank-Wolfe (Acc-SZOFW*) based on a new variance reduced technique of STORM, which still reaches the function query complexity of O(d^-3) in the stochastic problem without relying on any large batches. In particular, we present an accelerated framework of the Frank-Wolfe methods based on the proposed momentum accelerated technique. The extensive experimental results on black-box adversarial attack and robust black-box classification demonstrate the efficiency of our algorithms.

Tasks

Reproductions