  Although adversarial examples and model robustness have been extensively
studied in the context of linear models and neural networks, research on this
issue in tree-based models and how to make tree-based models robust against
adversarial examples is still limited. In this paper, we show that tree based
models are also vulnerable to adversarial examples and develop a novel
algorithm to learn robust trees. At its core, our method aims to optimize the
performance under the worst-case perturbation of input features, which leads to
a max-min saddle point problem. Incorporating this saddle point objective into
the decision tree building procedure is non-trivial due to the discrete nature
of trees --- a naive approach to finding the best split according to this
saddle point objective will take exponential time. To make our approach
practical and scalable, we propose efficient tree building algorithms by
approximating the inner minimizer in this saddle point problem, and present
efficient implementations for classical information gain based trees as well as
state-of-the-art tree boosting models such as XGBoost. Experimental results on
real world datasets demonstrate that the proposed algorithms can substantially
improve the robustness of tree-based models against adversarial examples.
