Provable tradeoffs in adversarially robust classification

Understand

It is well known that machine learning methods can be vulnerable to adversarially-chosen perturbations of their inputs.

• Despite significant progress in the area, foundational open problems remain.
• In this paper, we address several key questions.
• We derive exact and approximate Bayes-optimal robust classifiers for the important setting of two- and three-class Gaussian classification problems with arbitrary imbalance, for $\ell_2$ and $\ell_\infty$ adversaries.