We identify a trade-off between robustness and accuracy that serves as a guiding principle in the design of defenses against adversarial examples. Although this problem has been widely studied empirically, much remains unknown concerning the theory underlying this trade-off. In this work, we decompose the prediction error for adversarial examples (robust error) as the sum of the natural (classification) error and boundary error, and provide a differentiable upper bound using the theory of classification-calibrated loss, which is shown to be the tightest possible upper bound uniform over all probability distributions and measurable predictors. Inspired by our theoretical analysis, we also design a new defense method, TRADES, to trade adversarial robustness off against accuracy. Our proposed algorithm performs well experimentally in real-world datasets. The methodology is the foundation of our entry to the NeurIPS 2018 Adversarial Vision Challenge in which we won the 1st place out of 2,000 submissions, surpassing the runner-up approach by @math in terms of mean @math perturbation distance.
Compared with attack methods, adversarial defense methods are relatively fewer. Robust optimization based defenses are inspired by the above-mentioned attacks. Intuitively, the methods train a network by fitting its parameters to the adversarial examples: Following this framework, @cite_20 @cite_43 considered one-step adversaries, while @cite_55 worked with multi-step methods for the inner maximization problem. There are, however, two critical differences between the robust optimization based defenses and the present paper. Firstly, robust optimization based defenses lack of theoretical guarantees. Secondly, such methods do not consider the trade-off between accuracy and robustness.
@cite_43 @cite_55 @cite_20
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Abstract We show that adversarial training of supervised learning models is in fact a robust optimization procedure. To do this, we establish a general framework for increasing local stability of supervised learning models using robust optimization. The framework is general and broadly applicable to differentiable non-parametric models, e.g., Artificial Neural Networks (ANNs). Using an alternating minimization-maximization procedure, the loss of the model is minimized with respect to perturbed examples that are generated at each parameter update, rather than with respect to the original training data. Our proposed framework generalizes adversarial training, as well as previous approaches for increasing local stability of ANNs. Experimental results reveal that our approach increases the robustness of the network to existing adversarial examples, while making it harder to generate new ones. Furthermore, our algorithm improves the accuracy of the networks also on the original test data. Recent work has demonstrated that neural networks are vulnerable to adversarial examples, i.e., inputs that are almost indistinguishable from natural data and yet classified incorrectly by the network. To address this problem, we study the adversarial robustness of neural networks through the lens of robust optimization. This approach provides us with a broad and unifying view on much prior work on this topic. Its principled nature also enables us to identify methods for both training and attacking neural networks that are reliable and, in a certain sense, universal. In particular, they specify a concrete security guarantee that would protect against a well-defined class of adversaries. These methods let us train networks with significantly improved resistance to a wide range of adversarial attacks. They also suggest robustness against a first-order adversary as a natural and broad security guarantee. We believe that robustness against such well-defined classes of adversaries is an important stepping stone towards fully resistant deep learning models. The robustness of neural networks to intended perturbations has recently attracted significant attention. In this paper, we propose a new method, , that learns robust classifiers from supervised data. The proposed method takes finding adversarial examples as an intermediate step. A new and simple way of finding adversarial examples is presented and experimentally shown to be efficient. Experimental results demonstrate that resulting learning method greatly improves the robustness of the classification models produced.