Interpolation can hurt robust generalization even when there is no noise

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.

Two related workshop papers presented earlier:

• Surprising benefits of ridge regularization for noiseless regression — ICML 2021 Workshop on Overparameterization: Pitfalls and Opportunities
• Maximizing the robust margin provably overfits on noiseless data — ICML 2021 Workshop on Adversarial Machine Learning

@article{donhauser2021interpolation,
    title={Interpolation can hurt robust generalization even when there is no noise},
    author={Donhauser, Konstantin and Ţifrea, Alexandru and Aerni, Michael and Heckel, Reinhard and Yang, Fanny},
    booktitle={{Advances in Neural Information Processing Systems (NeurIPS)}},
    year={2021}
}