[edit]
Accelerated Stochastic Gradient-free and Projection-free Methods
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:4519-4530, 2020.
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(d√nϵ−2) for finding an ϵ-stationary point in the finite-sum problem, which improves the exiting best result by a factor of O(√nϵ−2), and has the function query complexity of O(dϵ−3) in the stochastic problem, which improves the exiting best result by a factor of O(ϵ−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(dϵ−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.