The adaptive momentum method (AdaMM), which uses past gradients to update descent directions and learning rates simultaneously, has become one of the most popular first-order optimization methods for solving machine learning problems. However, AdaMM is not suited for solving black-box optimization problems, where explicit gradient forms are difficult or infeasible to obtain. In this paper, we propose a zeroth-order AdaMM (ZO-AdaMM) algorithm, that generalizes AdaMM to the gradient-free regime. We show that the convergence rate of ZO-AdaMM for both convex and nonconvex optimization is roughly a factor of O(vd) worse than that of the first-order AdaMM algorithm, where d is problem size. In particular, we provide a deep understanding on why Mahalanobis distance matters in convergence of ZO-AdaMM and other AdaMM-type methods. As a byproduct, our analysis makes the first step toward understanding adaptive learning rate methods for nonconvex constrained optimization. Furthermore, we demonstrate two applications, designing per-image and universal adversarial attacks from blackbox neural networks, respectively. We perform extensive experiments on ImageNet and empirically show that ZO-AdaMM converges much faster to a solution of high accuracy compared with 6 state-of-the-art ZO optimization methods.
|Original language||English (US)|
|Journal||Advances in Neural Information Processing Systems|
|State||Published - 2019|
|Event||33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019 - Vancouver, Canada|
Duration: Dec 8 2019 → Dec 14 2019
Bibliographical noteFunding Information:
This work is partly supported by National Science Foundation CNS-1932351. M. Hong is supported in part by NSF under Grant CMMI-172775, CIF-1910385 and by ARO under grant 73202-CS.
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