Theoretical Foundations of Adversarially Robust Learning
Omar Montasser
Despite extraordinary progress, current machine learning systems have been
shown to be brittle against adversarial examples: seemingly innocuous but
carefully crafted perturbations of test examples that cause machine learning
predictors to misclassify. Can we learn predictors robust to adversarial
examples? and how? There has been much empirical interest in this contemporary
challenge in machine learning, and in this thesis, we address it from a
theoretical perspective.
  In this thesis, we explore what robustness properties can we hope to
guarantee against adversarial examples and develop an understanding of how to
algorithmically guarantee them. We illustrate the need to go beyond traditional
approaches and principles such as empirical risk minimization and uniform
convergence, and make contributions that can be categorized as follows: (1)
introducing problem formulations capturing aspects of emerging practical
challenges in robust learning, (2) designing new learning algorithms with
provable robustness guarantees, and (3) characterizing the complexity of robust
learning and fundamental limitations on the performance of any algorithm.