Overparameterized Linear Regression under Adversarial Attacks

We study the error of linear regression in face adversarial attacks. In this framework, an adversary changes input to model order maximize prediction error. provide bounds on presence as a function parameter norm and absence such adversary. show how these make it possible using analysis from non-adversarial setups. The obtained results shed light robustness overparameterized models Adding features might be either source additional or brittleness. On one hand, we use asymptotic illustrate double-descent curves can for other derive conditions under which grow infinity more are added, while at same time, test goes zero. behavior is caused by fact that vector grows with number features. It also established $\ell_\infty$ $\ell_2$-adversarial attacks behave fundamentally differently due $\ell_1$ $\ell_2$-norms random projections concentrate. our reformulation allows solving training convex optimization problem. This then exploited establish similarities between parameter-shrinking methods affect estimated models.