Interpolation can hurt robust generalization even when there is no noiseDownload PDF

21 May 2021, 20:52 (modified: 05 Nov 2021, 13:11)NeurIPS 2021 PosterReaders: Everyone
Keywords: regularization, high dimensional statistics, learning theory, robustness
TL;DR: We reveal unexpected benefits of regularization even in the overparameterized regime by proving that for both linear regression and classification, avoiding interpolation significantly improves generalization.
Abstract: 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 \emph{robust overfitting}.
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