Optimal Decision Tree Policies for Markov Decision Processes
This addresses the need for interpretable reinforcement learning policies in real-world tasks, though it is incremental as it builds on existing methods for decision tree optimization.
The authors tackled the problem of learning interpretable, rule-based policies for Markov Decision Processes (MDPs) by proposing OMDTs, which directly optimize decision trees for expected discounted return using Mixed-Integer Linear Programming, achieving performance close to the optimal limit with depth-3 trees.
Interpretability of reinforcement learning policies is essential for many real-world tasks but learning such interpretable policies is a hard problem. Particularly rule-based policies such as decision trees and rules lists are difficult to optimize due to their non-differentiability. While existing techniques can learn verifiable decision tree policies there is no guarantee that the learners generate a decision that performs optimally. In this work, we study the optimization of size-limited decision trees for Markov Decision Processes (MPDs) and propose OMDTs: Optimal MDP Decision Trees. Given a user-defined size limit and MDP formulation OMDT directly maximizes the expected discounted return for the decision tree using Mixed-Integer Linear Programming. By training optimal decision tree policies for different MDPs we empirically study the optimality gap for existing imitation learning techniques and find that they perform sub-optimally. We show that this is due to an inherent shortcoming of imitation learning, namely that complex policies cannot be represented using size-limited trees. In such cases, it is better to directly optimize the tree for expected return. While there is generally a trade-off between the performance and interpretability of machine learning models, we find that OMDTs limited to a depth of 3 often perform close to the optimal limit.