Hyperparameter Learning under Data Poisoning: Analysis of the Influence of Regularization via Multiobjective Bilevel Optimization

Machine Learning (ML) algorithms are vulnerable to poisoning attacks, where a fraction of the training data is manipulated to deliberately degrade the algorithms' performance. Optimal attacks can be formulated as bilevel optimization problems and help to assess their robustness in worst-case scenarios. We show that current approaches, which typically assume that hyperparameters remain constant, lead to an overly pessimistic view of the algorithms' robustness and of the impact of regularization. We propose a novel optimal attack formulation that considers the effect of the attack on the hyperparameters and models the attack as a multiobjective bilevel optimization problem. This allows to formulate optimal attacks, learn hyperparameters and evaluate robustness under worst-case conditions. We apply this attack formulation to several ML classifiers using $L_2$ and $L_1$ regularization. Our evaluation on multiple datasets confirms the limitations of previous strategies and evidences the benefits of using $L_2$ and $L_1$ regularization to dampen the effect of poisoning attacks.