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The problem of adversarial robustness has been studied extensively for neuralnetworks. However, for boosted decision trees and decision stumps there arealmost no results, even though they are widely used in practice (e.g. XGBoost)due to their accuracy, interpretability, and efficiency. We show in this paperthat for boosted decision stumps the \textit{exact} min-max robust loss andtest error for an $l_\infty$-attack can be computed in $O(T\log T)$ time perinput, where $T$ is the number of decision stumps and the optimal update stepof the ensemble can be done in $O(n^2\,T\log T)$, where $n$ is the number ofdata points. For boosted trees we show how to efficiently calculate andoptimize an upper bound on the robust loss, which leads to state-of-the-artrobust test error for boosted trees on MNIST (12.5% for $\epsilon_\infty=0.3$),FMNIST (23.2% for $\epsilon_\infty=0.1$), and CIFAR-10 (74.7% for$\epsilon_\infty=8/255$). Moreover, the robust test error rates we achieve arecompetitive to the ones of provably robust convolutional networks. The code ofall our experiments is available athttp://github.com/max-andr/provably-robust-boosting

Provably Robust Boosted Decision Stumps and Trees against Adversarial Attacks