Necessary and Sufficient Conditions for Optimal Decision Trees using Dynamic Programming

Published: 21 Sept 2023, Last Modified: 15 Jan 2024NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: optimal decision trees, dynamic programming, separability
TL;DR: We develop a general dynamic programming framework that can find optimal decision trees for any separable objective or constraint
Abstract: 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.
Submission Number: 6588