# Algebraically Explainable Controllers: Decision Trees and Support Vector Machines Join Forces

arXiv: https://arxiv.org/abs/2208.12804 · HTML: https://mlsanity.com/paper/2208.12804/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 54 references that are in the map.
- First posted on arXiv 26 Aug 2022.

## Builds on (most cited first, 9 of 9)

- [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)
- [SOS: Safe, Optimal and Small Strategies for Hybrid Markov Decision Processes](https://mlsanity.com/paper/1906.10640/) (2019)
- [Strategy Representation by Decision Trees with Linear Classifiers](https://mlsanity.com/paper/1906.08178/) (2019)
- [Optimal Symbolic Controllers Determinization for BDD storage](https://mlsanity.com/paper/1803.07369/) (2018)
- [Software Fault Tolerance for Cyber-Physical Systems via Full System Restart](https://mlsanity.com/paper/1812.03546/) (2018)
- [Compositional Synthesis of Symbolic Models for Networks of Switched Systems](https://mlsanity.com/paper/1905.12808/) (2019)

## Built on by (most cited first, 5 of 5)

- [Taming Infinity one Chunk at a Time: Concisely Represented Strategies in One-Counter MDPs](https://mlsanity.com/paper/2503.00788/) (2025)
- [Explaining Control Policies through Predicate Decision Diagrams](https://mlsanity.com/paper/2503.06420/) (2025)
- [ODTE -- An ensemble of multi-class SVM-based oblique decision trees](https://mlsanity.com/paper/2411.13376/) (2024)
- [Explainably Safe Reinforcement Learning](https://mlsanity.com/paper/2606.04634/) (2026)
- [dtControl2+varepsilon: Trading Optimality for Explainability in MDPs via Decision Trees](https://mlsanity.com/paper/2607.25925/) (2026)

## Abstract (arXiv)

Recently, decision trees (DT) have been used as an explainable representation of controllers (a.k.a. strategies, policies, schedulers). Although they are often very efficient and produce small and understandable controllers for discrete systems, complex continuous dynamics still pose a challenge. In particular, when the relationships between variables take more complex forms, such as polynomials, they cannot be obtained using the available DT learning procedures. In contrast, support vector machines provide a more powerful representation, capable of discovering many such relationships, but not in an explainable form. Therefore, we suggest to combine the two frameworks in order to obtain an understandable representation over richer, domain-relevant algebraic predicates. We demonstrate and evaluate the proposed method experimentally on established benchmarks.