Adaptive Regularization for Adversarial Training

Adversarial training, which is to enhance robustness against adversarial attacks, has received much attention because it is easy to generate human-imperceptible perturbations of data to deceive a given deep neural network. In this paper, we propose a new adversarial training algorithm that is theoretically well motivated and empirically superior to other existing algorithms. A novel feature of the proposed algorithm is to use a data-adaptive regularization for robustifying a prediction model. We apply more regularization to data which are more vulnerable to adversarial attacks and vice versa. Even though the idea of data-adaptive regularization is not new, our data-adaptive regularization has a firm theoretical base of reducing an upper bound of the robust risk. Numerical experiments illustrate that our proposed algorithm improves the generalization (accuracy on clean samples) and robustness (accuracy on adversarial attacks) simultaneously to achieve the state-of-the-art performance.