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Interpretability of AI models allows for user safety checks to build trust insuch AIs. In particular, Decision Trees (DTs) provide a global look at thelearned model and transparently reveal which features of the input are criticalfor making a decision. However, interpretability is hindered if the DT is toolarge. To learn compact trees, a recent Reinforcement Learning (RL) frameworkhas been proposed to explore the space of DTs using deep RL. This frameworkaugments a decision problem (e.g. a supervised classification task) withadditional actions that gather information about the features of an otherwisehidden input. By appropriately penalizing these actions, the agent learns tooptimally trade-off size and performance of DTs. In practice, a reactive policyfor a partially observable Markov decision process (MDP) needs to be learned,which is still an open problem. We show in this paper that deep RL can faileven on simple toy tasks of this class. However, when the underlying decisionproblem is a supervised classification task, we show that finding the optimaltree can be cast as a fully observable Markov decision problem and be solvedefficiently, giving rise to a new family of algorithms for learning DTs that gobeyond the classical greedy maximization ones.

Limits of Actor-Critic Algorithms for Decision Tree Policies Learning in IBMDPs