Adversarially Robust Generalization Requires More Data

Authors:
Ludwig Schmidt MIT
Shibani Santurkar MIT
Dimitris Tsipras MIT
Kunal Talwar Google
Aleksander Madry MIT

Introduction:

Machine learning models are often susceptible to adversarial perturbations of their inputs.To better understand this phenomenon, the authors study adversarially robust learning from the viewpoint of generalization.

Abstract:

Machine learning models are often susceptible to adversarial perturbations of their inputs. Even small perturbations can cause state-of-the-art classifiers with high "standard" accuracy to produce an incorrect prediction with high confidence. To better understand this phenomenon, we study adversarially robust learning from the viewpoint of generalization. We show that already in a simple natural data model, the sample complexity of robust learning can be significantly larger than that of "standard" learning. This gap is information theoretic and holds irrespective of the training algorithm or the model family. We complement our theoretical results with experiments on popular image classification datasets and show that a similar gap exists here as well. We postulate that the difficulty of training robust classifiers stems, at least partially, from this inherently larger sample complexity.

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