Interpolation can hurt robust generalization even when there is no noise

Konstantin Donhauser, Alexandru Tifrea, Michael Aerni, Reinhard Heckel, Fanny Yang

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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Code: https://github.com/michaelaerni/interpolation_robustness

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2108.02883/code)