Learning Optimal Decision Trees with SAT

Explanations of machine learning (ML) predictions are of fundamental importance in different settings. Moreover, explanations should be succinct, to enable easy understanding by human decision makers. Decision trees represent an often used approach for developing explainable ML models, motivated by the natural mapping between decision tree paths and rules. Clearly, smaller trees translate directly to smaller rules, and so one challenge is to devise solutions for computing smallest size decision trees given training data. Although simple to formulate, the computation of smallest size decision trees turns out to be an extremely challenging computational problem, for which no practical solutions are known. This paper develops a SAT-based model for computing smallest-size decision trees given training data. In sharp contrast with past work, the proposed SAT model is shown to scale for publicly available datasets of practical interest.