Impact statement: Learning predictors that are robust to adversarial perturbations is an important challenge in contem- porary machine learning. Current machine learning systems have been shown to be brittle against different notions of robustness such as adversarial perturbations [Szegedy et al., 2013, Biggio et al., 2013, Goodfellow et al., 2014], and there is an ongoing effort to devise methods for learning predictors that are adversarially robust. As machine learning systems become increasingly integrated into our everyday lives, it becomes crucial to provide guarantees about their performance, even when they are used outside their intended conditions. We already have many tools developed for standard learning, and having a universal wrapper that can take any standard learning method and turn it into a robust learning method could greatly simplify the development and deployment of learning that is robust to test-time adversarial perturbations. The results that we present in this paper are still mostly theoretical, and limited to the realizable setting, but we expect and hope they will lead to further theoretical study as well as practical methodological development with direct impact on applications. In this work we do not deal with training-time adversarial attacks, which is a major, though very different, concern in many cases. As with any technology, having a more robust technology can have positive and negative societal consequences, and this depends mainly on how such technology is utilized. Our intent from this research is to help with the design of robust machine learning systems for application domains such as healthcare and transportation where its critical to ensure performance guarantees even outside intended conditions. In situations where there is a tradeoff between robustness and accuracy, this work might be harmful in that it would prioritize robustness over accuracy and this may not be ideal in some application domains.