Interpolation can hurt robust generalization even when there is no noise
This addresses the problem of robust overfitting in machine learning, providing theoretical insights for practitioners dealing with adversarial robustness, though it is incremental in building on prior work on overparameterization.
The paper challenges the view that overparameterization reduces the need for ridge regularization by showing that avoiding interpolation through ridge regularization can significantly improve robust generalization, even without noise, for linear regression and classification.
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.