  In recent years, studies such as
\cite{carmon2019unlabeled,gowal2021improving,xing2022artificial} have
demonstrated that incorporating additional real or generated data with
pseudo-labels can enhance adversarial training through a two-stage training
approach. In this paper, we perform a theoretical analysis of the asymptotic
behavior of this method in high-dimensional linear regression. While a
double-descent phenomenon can be observed in ridgeless training, with an
appropriate $\mathcal{L}_2$ regularization, the two-stage adversarial training
achieves a better performance. Finally, we derive a shortcut cross-validation
formula specifically tailored for the two-stage training method.
