Robustness Verification of Tree-based Models

TL;DR

This paper introduces a novel, efficient algorithm for verifying the robustness of tree-based models, significantly outperforming previous MILP-based methods and providing tight bounds on model robustness.

Contribution

It presents a new polynomial-time verification algorithm for single trees and a multi-level approach for ensembles, exploiting graph properties to improve efficiency and accuracy.

Findings

Algorithm is hundreds of times faster than MILP-based methods.

Provides tight robustness bounds for large GBDT models.

Applicable to decision trees, RFs, and GBDTs across multiple datasets.

Abstract

We study the robustness verification problem for tree-based models, including decision trees, random forests (RFs) and gradient boosted decision trees (GBDTs). Formal robustness verification of decision tree ensembles involves finding the exact minimal adversarial perturbation or a guaranteed lower bound of it. Existing approaches find the minimal adversarial perturbation by a mixed integer linear programming (MILP) problem, which takes exponential time so is impractical for large ensembles. Although this verification problem is NP-complete in general, we give a more precise complexity characterization. We show that there is a simple linear time algorithm for verifying a single tree, and for tree ensembles, the verification problem can be cast as a max-clique problem on a multi-partite graph with bounded boxicity. For low dimensional problems when boxicity can be viewed as constant, this reformulation leads to a polynomial time algorithm. For general problems, by exploiting the boxicity of the graph, we develop an efficient multi-level verification algorithm that can give tight lower bounds on the robustness of decision tree ensembles, while allowing iterative improvement and any-time termination. OnRF/GBDT models trained on 10 datasets, our algorithm is hundreds of times faster than the previous approach that requires solving MILPs, and is able to give tight robustness verification bounds on large GBDTs with hundreds of deep trees.