Necessary and Sufficient Conditions for Optimal Decision Trees using Dynamic Programming

TL;DR

This paper establishes the necessary and sufficient conditions for optimizing decision trees with dynamic programming, presenting a generalized framework that improves scalability and applicability across various domains.

Contribution

It identifies the conditions for objective separability in decision tree optimization and generalizes dynamic programming methods into a versatile framework.

Findings

Framework outperforms general-purpose solvers in scalability

Applicable to multiple application domains

Handles various separable objectives and constraints

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.