Robust machine learning formulations have emerged to address the prevalent vulnerability of deep neural networks to adversarial examples. Our work draws the connection between optimal robust learning and the privacy-utility tradeoff problem, which is a generalization of the rate-distortion problem. The saddle point of the game between a robust classifier and an adversarial perturbation can be found via the solution of a maximum conditional entropy problem. This information-theoretic perspective sheds light on the fundamental tradeoff between robustness and clean data performance, which ultimately arises from the geometric structure of the underlying data distribution and perturbation constraints.