# Explaining Control Policies through Predicate Decision Diagrams

arXiv: https://arxiv.org/abs/2503.06420 · HTML: https://mlsanity.com/paper/2503.06420/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 71 references that are in the map.
- First posted on arXiv 9 Mar 2025.

## Builds on (most cited first, 14 of 14)

- [A storm is Coming: A Modern Probabilistic Model Checker](https://mlsanity.com/paper/1702.04311/) (2017)
- [dtControl 2.0: Explainable Strategy Representation via Decision Tree Learning Steered by Experts](https://mlsanity.com/paper/2101.07202/) (2021)
- [dtControl: Decision Tree Learning Algorithms for Controller Representation](https://mlsanity.com/paper/2002.04991/) (2020)
- [Counterexample Explanation by Learning Small Strategies in Markov Decision Processes](https://mlsanity.com/paper/1502.02834/) (2015)
- [Optimal Decision Diagrams for Classification](https://mlsanity.com/paper/2205.14500/) (2022)
- [SOS: Safe, Optimal and Small Strategies for Hybrid Markov Decision Processes](https://mlsanity.com/paper/1906.10640/) (2019)
- [Optimal Decision Tree Policies for Markov Decision Processes](https://mlsanity.com/paper/2301.13185/) (2023)
- [SPUDD: Stochastic Planning using Decision Diagrams](https://mlsanity.com/paper/1301.6704/) (2013)
- [Optimizing Binary Decision Diagrams with MaxSAT for classification](https://mlsanity.com/paper/2203.11386/) (2022)
- [Strategy Representation by Decision Trees in Reactive Synthesis](https://mlsanity.com/paper/1802.00758/) (2018)
- [Algebraically Explainable Controllers: Decision Trees and Support Vector Machines Join Forces](https://mlsanity.com/paper/2208.12804/) (2022)
- [Optimal Symbolic Controllers Determinization for BDD storage](https://mlsanity.com/paper/1803.07369/) (2018)
- [Learning-Based Synthesis of Safety Controllers](https://mlsanity.com/paper/1901.06801/) (2019)
- [Synthesizing Pareto-Optimal Interpretations for Black-Box Models](https://mlsanity.com/paper/2108.07307/) (2021)

## Built on by (most cited first, 1 of 1)

- [dtControl2+varepsilon: Trading Optimality for Explainability in MDPs via Decision Trees](https://mlsanity.com/paper/2607.25925/) (2026)

## Abstract (arXiv)

Safety-critical controllers of complex systems are hard to construct manually. Automated approaches such as controller synthesis or learning provide a tempting alternative but usually lack explainability. To this end, learning decision trees (DTs) have been prevalently used towards an interpretable model of the generated controllers. However, DTs do not exploit shared decision-making, a key concept exploited in binary decision diagrams (BDDs) to reduce their size and thus improve explainability. In this work, we introduce predicate decision diagrams (PDDs) that extend BDDs with predicates and thus unite the advantages of DTs and BDDs for controller representation. We establish a synthesis pipeline for efficient construction of PDDs from DTs representing controllers, exploiting reduction techniques for BDDs also for PDDs.