Optimal Robust Decision Trees
A dynamic programming approach
A.B.C. Bien (TU Delft - Electrical Engineering, Mathematics and Computer Science)
E. Demirović – Graduation committee member (TU Delft - Algorithmics)
J.G.M. van der Linden – Mentor (TU Delft - Algorithmics)
B. Özkan – Graduation committee member (TU Delft - Software Engineering)
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Abstract
Decision trees are integral to machine learning, with their robustness being a critical measure of effectiveness against adversarial data manipulations. Despite advancements in algorithms, current solutions are either optimal but lack scalability or scale well, but do not guarrantee optimality. This paper presents a novel adaptation of the Murtree algorithm to address these challenges in the pursuit of optimal robust decision trees. We introduce a new method for modeling an adversary as a network flow problem, and provide a dynamic programming approach to solve optimal robust decision trees beyond a depth of two. The performance of our proposed algorithm is compared with bruteforce solutions across varying decision tree depths, feature numbers, and data sizes. This research contributes a significant advancement towards obtaining efficient and effective solutions for optimal robust decision trees, potentially setting a new performance benchmark in this area.