Semi-Implicit Hybrid Gradient Methods with Application to Adversarial Robustness
This work addresses the challenge of adversarial robustness in deep learning, offering a faster and more robust training method, though it is incremental as it builds on existing adversarial training algorithms.
The paper tackles the problem of training adversarially robust deep neural networks by developing semi-implicit hybrid gradient methods (SI-HGs) for nonconvex-nonconcave minimax problems, achieving a convergence rate of O(1/K) that improves upon prior methods like DAT and YOPO with O(1/K^{1/2}), and demonstrating superior performance in convergence speed and robustness.
Adversarial examples, crafted by adding imperceptible perturbations to natural inputs, can easily fool deep neural networks (DNNs). One of the most successful methods for training adversarially robust DNNs is solving a nonconvex-nonconcave minimax problem with an adversarial training (AT) algorithm. However, among the many AT algorithms, only Dynamic AT (DAT) and You Only Propagate Once (YOPO) guarantee convergence to a stationary point. In this work, we generalize the stochastic primal-dual hybrid gradient algorithm to develop semi-implicit hybrid gradient methods (SI-HGs) for finding stationary points of nonconvex-nonconcave minimax problems. SI-HGs have the convergence rate $O(1/K)$, which improves upon the rate $O(1/K^{1/2})$ of DAT and YOPO. We devise a practical variant of SI-HGs, and show that it outperforms other AT algorithms in terms of convergence speed and robustness.