Necessary and Sufficient Conditions for Optimal Decision Trees using Dynamic Programming

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

Bibtex Paper


Jacobus van der Linden, Mathijs de Weerdt, Emir Demirović


Global optimization of decision trees has shown to be promising in terms of accuracy, size, and consequently human comprehensibility. However, many of the methods used rely on general-purpose solvers for which scalability remains an issue.Dynamic programming methods have been shown to scale much better because they exploit the tree structure by solving subtrees as independent subproblems. However, this only works when an objective can be optimized separately for subtrees.We explore this relationship in detail and show the necessary and sufficient conditions for such separability and generalize previous dynamic programming approaches into a framework that can optimize any combination of separable objectives and constraints.Experiments on five application domains show the general applicability of this framework, while outperforming the scalability of general-purpose solvers by a large margin.