Branches: Efficiently Seeking Optimal Sparse Decision Trees with AO*

Abstract

Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch & Bound. However, most of these approaches rely on a Depth-First-Search strategy, which is inefficient when searching for DTs at high depths and requires the definition of a maximum depth hyperparameter. Best-First-Search was also employed by other methods to circumvent these issues. The downside of this strategy is its higher memory consumption, as such, it has to be designed in a fully efficient manner that takes full advantage of the problem's structure. We formulate the problem within an AND/OR graph search framework and we solve it with a novel AO*-type algorithm called Branches. We prove both optimality and complexity guarantees for Branches and we show that it is more efficient than the state of the art theoretically and on a variety of experiments. Furthermore, Branches supports non-binary features unlike the other methods, we show that this property can further induce larger gains in computational efficiency.

Proceedings of the 42nd International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025