论文标题
在$ \ ell_p $ - 合奏树桩和树木的鲁棒性
On $\ell_p$-norm Robustness of Ensemble Stumps and Trees
论文作者
论文摘要
最近的论文表明,整体树桩和树木可能容易受到小型输入扰动的影响,因此这些模型的稳健性验证和防御已成为一个重要的研究问题。但是,由于决策树的结构,每个节点纯粹基于一个特征值制定决策,因此所有先前的作品仅考虑$ \ ell_ \ infty $ norm扰动。为了研究一般$ \ ell_p $ norm扰动的鲁棒性,必须考虑在不同特征上的扰动之间的相关性,而这些特征尚未通过以前的算法来处理。在本文中,我们研究了关于一般$ \ ell_p $ norm norm扰动的鲁棒性验证问题,并研究了整体决策树桩和树木的问题。为了对合奏树桩进行稳健性验证,我们证明(0,\ infty)$的$ p \ in Potal验证是NP的完整验证,而多项式时间算法则为$ p = 0 $或$ \ infty $。对于$ p \ in(0,\ infty)$,我们开发了一种有效的基于动态编程的算法,以验证集合树桩的声音验证。对于合奏树,我们将以前的多级鲁棒性验证算法推广到$ \ ell_p $ norm。我们演示了第一种与$ \ ell_p $ norm扰动有关的培训集合树桩和树木的认证防御方法,并在真实数据集上经验验证其有效性。
Recent papers have demonstrated that ensemble stumps and trees could be vulnerable to small input perturbations, so robustness verification and defense for those models have become an important research problem. However, due to the structure of decision trees, where each node makes decision purely based on one feature value, all the previous works only consider the $\ell_\infty$ norm perturbation. To study robustness with respect to a general $\ell_p$ norm perturbation, one has to consider the correlation between perturbations on different features, which has not been handled by previous algorithms. In this paper, we study the problem of robustness verification and certified defense with respect to general $\ell_p$ norm perturbations for ensemble decision stumps and trees. For robustness verification of ensemble stumps, we prove that complete verification is NP-complete for $p\in(0, \infty)$ while polynomial time algorithms exist for $p=0$ or $\infty$. For $p\in(0, \infty)$ we develop an efficient dynamic programming based algorithm for sound verification of ensemble stumps. For ensemble trees, we generalize the previous multi-level robustness verification algorithm to $\ell_p$ norm. We demonstrate the first certified defense method for training ensemble stumps and trees with respect to $\ell_p$ norm perturbations, and verify its effectiveness empirically on real datasets.