Learning in the Presence of Distribution Shifts: How does the Geometry of Perturbations Play a Role?

Hamed Hassani, Assistant Professor, University of Pennsylvania

Abstract: In this talk, we will focus on the emerging field of (adversarially) robust machine learning. The talk will be self-contained and no particular background on robust learning will be needed. Recent progress in this field has been accelerated by the observation that despite unprecedented performance on clean data, modern learning models remain fragile to seemingly innocuous changes such as small, norm-bounded additive perturbations. Moreover, recent work in this field has looked beyond norm-bounded perturbations and has revealed that various other types of distributional shifts in the data can significantly degrade performance. However, in general our understanding of such shifts is in its infancy and several key questions remain unaddressed.

The goal of this talk is to explain why robust learning paradigms have to be designed—and sometimes rethought—based on the geometry of the input perturbations. We will cover a wide range of perturbation geometries from simple norm-bounded perturbations, to sparse, natural, and more general distribution shifts. As we will show, the geometry of the perturbations necessitates fundamental modifications to the learning procedure as well as the architecture in order to ensure robustness. In the first part of the talk, we will discuss our recent theoretical results on robust learning with respect to various geometries, along with fundamental tradeoffs between robustness and accuracy, phase transitions, etc. The remaining portion of the talk will be about developing practical robust training algorithms and evaluating the resulting (robust) deep networks against state-of-the-art methods on naturally-varying, real-world datasets.