Numerous recent works show that overparameterization implicitly reduces variance for min-norm interpolators and max-margin classifiers. These findings suggest that ridge regularization has vanishing benefits in high dimensions. We challenge this narrative by showing that, even in the absence of noise, avoiding interpolation through ridge regularization can significantly improve generalization. We prove this phenomenon for the robust risk of both linear regression and classification and hence provide the first theoretical result on robust overfitting.

翻译：近期许多研究显示,过度参数化隐含地减少了中上层间插器和最大差值分类器的差异。 这些研究结果表明,山脊正规化的好处在高维方面消失殆尽。 我们质疑这一说法,表明即使在没有噪音的情况下,通过山脊正规化避免内插也能大大改善一般化。 我们证明这种现象具有线性回归和分类的强大风险,因此提供了稳健超标的第一个理论结果。