On the Adversarial Robustness of Decision Trees and a Symmetry Defense

Gradient-boosting decision tree classifiers (GBDTs) are susceptible to adversarial perturbation attacks that change inputs slightly to cause misclassification. GBDTs are customarily used on non-image datasets that lack inherent symmetries, which might be why data symmetry in the context of GBDT classifiers has not received much attention. In this paper, we show that GBDTs can classify symmetric samples differently, which means that GBDTs lack invariance with respect to symmetry. Based on this, we defend GBDTs against adversarial perturbation attacks using symmetric adversarial samples in order to obtain correct classification. We apply and evaluate the symmetry defense against six adversarial perturbation attacks on the GBDT classifiers of nine datasets with a threat model that ranges from zero-knowledge to perfect-knowledge adversaries. Against zero-knowledge adversaries, we use the feature inversion symmetry and exceed the accuracies of default and robust classifiers by up to 100% points. Against perfect-knowledge adversaries for the GBDT classifier of the F-MNIST dataset, we use the feature inversion and horizontal flip symmetries and exceed the accuracies of default and robust classifiers by up to 96% points. Finally, we show that the current definition of adversarial robustness based on the minimum perturbation values of misclassifying adversarial samples might be inadequate for two reasons. First, this definition assumes that attacks mostly succeed, failing to consider the case when attacks are unable to construct misclassifying adversarial samples against a classifier. Second, GBDT adversarial robustness as currently defined can decrease by training with additional samples, even training samples, which counters the common wisdom that more training samples should increase robustness. With the current definition of GBDT adversarial robustness, we can make GBDTs more adversarially robust by training them with fewer samples! The code is publicly available at https://github.com/blertal/xgboost-symmetry-defense.