  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.
