Robustness and generalization

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel approach, different from complexity or stability arguments, to study generalization of learning algorithms. One advantage of the robustness approach, compared to previous methods, is the geometric intuition it conveys. Consequently, robustness-based analysis is easy to extend to learning in non-standard setups such as Markovian samples or quantile loss. We further show that a weak notion of robustness is both sufficient and necessary for generalizability, which implies that robustness is a fundamental property that is required for learning algorithms to work.