Robustness to Adversarial Perturbations in Learning from Incomplete Data

What is the role of unlabeled data in an inference problem, when the presumed underlying distribution is adversarially perturbed? To provide a concrete answer to this question, this paper unifies two major learning frameworks: Semi-Supervised Learning (SSL) and Distributionally Robust Learning (DRL). We develop a generalization theory for our framework based on a number of novel complexity measures, such as an adversarial extension of Rademacher complexity and its semi-supervised analogue. Moreover, our analysis is able to quantify the role of unlabeled data in the generalization under a more general condition compared to the existing theoretical works in SSL. Based on our framework, we also present a hybrid of DRL and EM algorithms that has a guaranteed convergence rate.