Fast Training of Provably Robust Neural Networks by SingleProp

Recent works have developed several methods of defending neural networks against adversarial attacks with certified guarantees. However, these techniques can be computationally costly due to the use of certification during training. We develop a new regularizer that is both more efficient than existing certified defenses, requiring only one additional forward propagation through a network, and can be used to train networks with similar certified accuracy. Through experiments on MNIST and CIFAR-10 we demonstrate improvements in training speed and comparable certified accuracy compared to state-of-the-art certified defenses.

Higher-Order Certification for Randomized Smoothing

Randomized smoothing is a recently proposed defense against adversarial attacks that has achieved SOTA provable robustness against $ell_2$ perturbations. A number of publications have extended the guarantees to other metrics, such as $ell_1$ or $ell_infty$, by using different smoothing measures. Although the current framework has been shown to yield near-optimal $ell_p$ radii, the total safety region certified by the current framework can be arbitrarily small compared to the optimal. In this work, we propose a framework to improve the certified safety region for these smoothed classifiers without changing the underlying smoothing scheme. The theoretical contributions are as follows: 1) We generalize the certification for randomized smoothing by reformulating certified radius calculation as a nested optimization problem over a class of functions. 2) We provide a method to calculate the certified safety region using $0^{th}$-order and $1^{st}$-order information for Gaussian-smoothed classifiers. We also provide a framework that generalizes the calculation for certification using higher-order information. 3) We design efficient, high-confidence estimators for the relevant statistics of the first-order information. Combining the theoretical contribution 2) and 3) allows us to certify safety region that are significantly larger than the ones provided by the current methods. On CIFAR10 and Imagenet datasets, the new regions certified by our approach achieve significant improvements on general $ell_1$ certified radii and on the $ell_2$ certified radii for color-space attacks ($ell_2$ restricted to 1 channel) while also achieving smaller improvements on the general $ell_2$ certified radii. Our framework can also provide a way to circumvent the current impossibility results on achieving higher magnitude of certified radii without requiring the use of data-dependent smoothing techniques.

Robust Deep Reinforcement Learning through Adversarial Loss

Deep neural networks, including reinforcement learning agents, have been proven vulnerable to small adversarial changes in the input, thus making deploying such networks in the real world problematic. In this paper, we propose RADIAL-RL, a method to train reinforcement learning agents with improved robustness against any $l_p$-bounded adversarial attack. By simply minimizing an upper bound of the loss functions under worst case adversarial perturbation derived from efficient robustness verification methods, we significantly improve robustness of RL-agents trained on Atari-2600 games and show that RADIAL-RL can beat state-of-the-art robust training algorithms when evaluated against PGD-attacks. We also propose a new evaluation method, Greedy Worst-Case Reward (GWC), for measuring attack agnostic robustness of RL agents. GWC can be evaluated efficiently and it serves as a good estimate of the reward under the worst possible sequence of adversarial attacks; in particular, GWC accounts for the importance of each action and their temporal dependency, improving upon previous approaches that only evaluate whether each single action can change under input perturbations. Our code is available at https://github.com/tuomaso/radial_rl.