Discovering the Interpretability-Performance Pareto Front of Decision Trees with Dynamic Programming

Decision trees are known to be intrinsically interpretable as they can be inspected and interpreted by humans. Furthermore, recent hardware advances have rekindled an interest for optimal decision tree algorithms, that produce more accurate trees than the usual greedy approaches. However, these optimal algorithms return a single tree optimizing a hand defined interpretability-performance trade-off, obtained by specifying a maximum number of decision nodes, giving no further insights about the quality of this trade-off. In this paper, we propose a new Markov Decision Problem (MDP) formulation for finding optimal decision trees. The main interest of this formulation is that we can compute the optimal decision trees for several interpretability-performance trade-offs by solving a single dynamic program, letting the user choose a posteriori the tree that best suits their needs. Empirically, we show that our method is competitive with state-of-the-art algorithms in terms of accuracy and runtime while returning a whole set of trees on the interpretability-performance Pareto front.