The Noise Premium in Adversarial Training for Kernel Regression
Adversarial training can improve the robustness of predictive models to bounded perturbations, often at the cost of statistical efficiency. We study this trade-off in kernel regression over a reproducing kernel Hilbert space (RKHS). It is shown that, under squared loss, adversarial training in RKHS introduces a term involving the product of the function norm with the mean absolute value of the response noise, which we call the \textit{noise premium}. Our analysis shows that the noise premium makes the prediction error of adversarial training converge strictly more slowly than the nonparametric minimax benchmark even after balancing approximation and estimation errors. Moreover, for a fixe...
| Authors | Yiling Xie, Xiaoming Huo |
|---|---|
| Primary category | stat.ML |
| Published | 30 July 2026 |
| Last updated at source | 13 August 2026 |
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