Interpolation can hurt robust generalization even when there is no noise

Part of Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021)

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


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}.