Title: Amata: An Annealing Mechanism for Adversarial Training Acceleration. Abstract: Despite of the empirical success in various domains, it has been revealed that deep neural networks are vulnerable to maliciously perturbed input data that much degrade their performance. This is known as adversarial attacks. To counter adversarial attacks, adversarial training formulated as a form of robust optimization has been demonstrated to be effective. However, conducting adversarial training brings much computational overhead compared with standard training. In order to reduce the computational cost, we propose a simple yet effective modification to the commonly used projected gradient descent (PGD) adversarial training by increasing the number of adversarial training steps and decreasing the adversarial training step size gradually as training proceeds. We analyze the optimality of this annealing mechanism through the lens of optimal control theory, and we also prove the convergence of our proposed algorithm. Numerical experiments on standard datasets, such as MNIST and CIFAR10, show that our method can achieve similar or even better robustness with around 1/3 to 1/2 computation time compared with PGD.