On the Adversarial Robustness of Linear Regression

In this paper, we study the adversarial robustness of linear regression problems. Specifically, we investigate the robustness of the regression coefficients against adversarial data samples. In the considered model, there exists an adversary who is able to add one carefully designed adversarial data sample into the dataset. By leveraging this poisoned data sample, the adversary tries to boost or depress the magnitude of one targeted regression coefficient under the energy constraint of the adversarial data sample. We characterize the exact expression of the optimal adversarial data sample in terms of the targeted regression coefficient, the original dataset and the energy budget. Our experiments with synthetic and real datasets show the efficiency and optimality of our proposed adversarial strategy.