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.

本文研究在简单自然数据模型中，对抗鲁棒学习的样本复杂度可以显著大于标准学习，这个差距是信息理论的，且与训练算法或模型家族无关。作者做了一些实验来证实这个结果。我们可以假设训练鲁棒分类器的困难，至少部分来自这种固有的更大的样本复杂度。

对抗鲁棒性泛化需要更多数据