Several recent works have developed methods for training classifiers that are certifiably robust against norm-bounded adversarial perturbations. These methods assume that all the adversarial transformations are equally important, which is seldom the case in real-world applications. We advocate for cost-sensitive robustness as the criteria for measuring the classifier's performance for tasks where some adversarial transformation are more important than others. We encode the potential harm of each adversarial transformation in a cost matrix, and propose a general objective function to adapt the robust training method of Wong & Kolter (2018) to optimize for cost-sensitive robustness. Our experiments on simple MNIST and CIFAR10 models with a variety of cost matrices show that the proposed approach can produce models with substantially reduced cost-sensitive robust error, while maintaining classification accuracy.
A general method for training certified cost-sensitive robust classifier against adversarial perturbations Calculates and plugs in the costs of adversarial attack into the objective of optimization to get a model that is cost-sensitively robust against adversarial attacks.  Build on semnial work by Dalvi et al. and extends approach to certifiable robustness with a cost matrix that specifies for each pair of source-target classes whether the model should be robust to adversarial examples.