dtControl2+$\varepsilon$: Trading Optimality for Explainability in MDPs via Decision Trees

2026-07-28

AI Summary

This work addresses the challenge that decision tree–based controllers for Markov decision processes (MDPs), while interpretable, often become excessively large and unwieldy in complex systems. The authors propose a novel approach that integrates policy distillation, decision tree induction, and formal verification within the dtControl2 framework, introducing for the first time a user-specified accuracy loss parameter $\varepsilon$ to construct minimally sized decision trees with provable $\varepsilon$-optimality guarantees. By enabling users to trade a small, controlled amount of performance for substantial simplification in policy structure, the method offers a tunable interpretability–performance trade-off. Experimental results demonstrate that the resulting decision trees are orders of magnitude smaller than those produced by state-of-the-art methods while rigorously preserving $\varepsilon$-optimality, thereby significantly enhancing human comprehensibility of complex MDP policies.

Abstract

Over the past decade, decision trees have been used to represent controllers (a.k.a. policies) in an explainable way, with dtControl2 as a current state-of-the-art tool. However, for systems that are large or have many corner cases, even such representations tend to be too complex and not human-comprehensible. Unfortunately, reducing the size of the decision tree is not straightforward, as missing just a single crucial case might result in an incorrect controller. We tackle this issue in the setting of Markov decision processes, extending dtControl2 by "$\varepsilon$" functionality: Given an allowed imprecision $\varepsilon \geq 0$, we construct a smaller decision tree, distilling the essence of the controller, while still guaranteeing its $\varepsilon$-optimality. This enables us to provide tunably simpler explanations, omitting a controllable amount of detail. Our tool constructs decision trees that are orders of magnitude smaller than the state of the art.

Problem

• Markov decision processes
• decision trees
• explainability
• controller complexity
• human-comprehensibility

Innovation

• explainable AI
• decision trees
• Markov decision processes
• epsilon-optimality
• policy distillation