Title: Improving Adversarial Robustness of Deep Neural Networks via Self-adaptive Margin Defense. Abstract: Adversarial training has become the most popular and effective strategy to improve Deep Neural Network (DNN) robustness against adversarial noises. Many adversarial training methods have been proposed in the past few years. However, most adversarial training methods are highly susceptible to hyperparameters, especially the training noise upper bound. Tuning these parameters is expensive for large datasets and difficult for people not in the adversarial robustness research domain, which prevents adversarial training techniques from being used in many application fields. This paper introduces a new adversarial training method with a gradual expansion mechanism to generate adversarial training samples, and it is parameter-free for the user. By gradually expanding the exploration range with self-adaptive and gradient-aware step size, adversarial training samples can be placed into the optimal locations in the input data space. Unlike other defense methods that usually need to fine-tune hyperparameters (e.g., training noise upper bound) by grid-search, our method has no hyperparameters for the user. We name our method Self-adaptive Margin Defense (SMD). We evaluate SMD on three publicly available datasets (CIFAR10, SVHN, and Fashion-MNIST) under the most popular adversarial attacks, AutoAttack and PGD. The results show that: (1) compared with all other competing defense methods, SMD has the best overall performance in robust accuracy on noisy data; (2) the accuracy degradation of SMD on clean data is minor among all competing defense methods.