Semi-Implicit Hybrid Gradient Methods with Application to Adversarial Robustness (2202.10523v1)

Abstract: 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.