Dynamic Mixed Training
There is an arms race to defend neural networks against adversarial examples. Notably, adversarially robust training and verifiably robust training are the most promising defenses. The adversarially robust training scales well but cannot provide provable robustness guarantee for the absence of attacks. We present an Interval Attack that reveals fundamental problems about the threat model used by adversarially robust training. On the contrary, verifiably robust training achieves sound guarantee, but it is computationally expensive and sacrifices accuracy, which prevents it being applied in practice. In this paper, we propose two novel techniques for verifiably robust training, stochastic output approximation and dynamic mixed training, to solve the aforementioned challenges. They are based on two critical insights: (1) soundness is only needed in a subset of training data; and (2) verifiable robustness and test accuracy are conflicting to achieve after a certain point of verifiably robust training. On both MNIST and CIFAR datasets, we are able to achieve similar test accuracy and estimated robust accuracy against PGD attacks within $14\times$ less training time compared to state-of-the-art adversarially robust training techniques. In addition, we have up to 95.2% verified robust accuracy as a bonus. Also, to achieve similar verified robust accuracy, we are able to save up to $5\times$ computation time and offer 9.2% test accuracy improvement compared to current state-of-the-art verifiably robust training techniques. …

The Adam algorithm has become extremely popular for large-scale machine learning. Under convexity condition, it has been proved to enjoy a data-dependant $O(\sqrt{T})$ regret bound where $T$ is the time horizon. However, whether strong convexity can be utilized to further improve the performance remains an open problem. In this paper, we give an affirmative answer by developing a variant of Adam (referred to as SAdam) which achieves a data-dependant $O(\log T)$ regret bound for strongly convex functions. The essential idea is to maintain a faster decaying yet under controlled step size for exploiting strong convexity. In addition, under a special configuration of hyperparameters, our SAdam reduces to SC-RMSprop, a recently proposed variant of RMSprop for strongly convex functions, for which we provide the first data-dependent logarithmic regret bound. Empirical results on optimizing strongly convex functions and training deep networks demonstrate the effectiveness of our method. …