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Machine Learning (ML) algorithms are vulnerable to poisoning attacks, where afraction of the training data is manipulated to deliberately degrade thealgorithms' performance. Optimal attacks can be formulated as bileveloptimization problems and help to assess their robustness in worst-casescenarios. We show that current approaches, which typically assume thathyperparameters remain constant, lead to an overly pessimistic view of thealgorithms' robustness and of the impact of regularization. We propose a noveloptimal attack formulation that considers the effect of the attack on thehyperparameters and models the attack as a multiobjective bilevel optimizationproblem. This allows to formulate optimal attacks, learn hyperparameters andevaluate robustness under worst-case conditions. We apply this attackformulation to several ML classifiers using $L_2$ and $L_1$ regularization. Ourevaluation on multiple datasets confirms the limitations of previous strategiesand evidences the benefits of using $L_2$ and $L_1$ regularization to dampenthe effect of poisoning attacks.

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