This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds in two directions, to solve an open problem that has seen little development since 2010. The first is to reduce the dependence on the covering number. The second is to remove the dependence on the hypothesis space. We present several examples, including ones for lasso and deep learning, in which our bounds are provably preferable. The experiments on real-world data and theoretical models demonstrate near-exponential improvements in various situations. To achieve these improvements, we do not require additional assumptions on the unknown distribution; instead, we only incorporate an observable and computable property of the training samples. A key technical innovation is an improved concentration bound for multinomial random variables that is of independent interest beyond robustness and generalization.

翻译：本文证明,稳健性意味着通过依赖数据的一般化界限进行一般化。 因此, 稳健性和一般化被证明以依赖数据的方式密切关联。 我们的界限在两个方向上改进了先前的界限, 以解决一个自2010年以来发展甚微的开放问题。 第一个是减少对覆盖数字的依赖。 第二个是消除对假设空间的依赖。 我们举了几个例子, 包括拉索和深层次学习的例子, 我们的界限是相当可取的。 现实世界数据和理论模型的实验表明, 各种情况都有近乎迅速的改进。 为了实现这些改进, 我们不需要对未知分布进行更多的假设; 相反, 我们只需要对培训样品的可观测和可计算属性进行整合。 一个关键的技术创新是, 将多数值随机变量的浓度进一步集中, 后者具有独立的兴趣, 超出了稳健性和概括性。