  We study the problem of robust learning against adversarial perturbations
under cost-sensitive scenarios, where the potential harm of different types of
misclassifications is encoded in a cost matrix. Existing approaches are either
empirical and cannot certify robustness or suffer from inherent scalability
issues. In this work, we investigate whether randomized smoothing, a scalable
framework for robustness certification, can be leveraged to certify and train
for cost-sensitive robustness. Built upon the notion of cost-sensitive
certified radius, we first illustrate how to adapt the standard certification
algorithm of randomized smoothing to produce tight robustness certificates for
any binary cost matrix, and then develop a robust training method to promote
certified cost-sensitive robustness while maintaining the model's overall
accuracy. Through extensive experiments on image benchmarks, we demonstrate the
superiority of our proposed certification algorithm and training method under
various cost-sensitive scenarios. Our implementation is available as open
source code at: https://github.com/TrustMLRG/CS-RS.
