# Mo"ET: Mixture of Expert Trees and its Application to Verifiable Reinforcement Learning

arXiv: https://arxiv.org/abs/1906.06717 · HTML: https://mlsanity.com/paper/1906.06717/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in MoE in reinforcement learning and robotics, one of 12 directions in Mixture-of-experts.
- Builds on 14 of its 62 references that are in the map.
- First posted on arXiv 16 Jun 2019.

## Placed in

- Mixture-of-experts / [MoE in reinforcement learning and robotics](https://mlsanity.com/moe/moe-in-reinforcement-learning-and-robotics/)

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

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Born Again Neural Networks](https://mlsanity.com/paper/1805.04770/) (2018)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Verifiable Reinforcement Learning via Policy Extraction](https://mlsanity.com/paper/1805.08328/) (2018)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [Explainable Machine Learning for Scientific Insights and Discoveries](https://mlsanity.com/paper/1905.08883/) (2019)
- [Learning Finite State Representations of Recurrent Policy Networks](https://mlsanity.com/paper/1811.12530/) (2018)
- [Formal Verification of Input-Output Mappings of Tree Ensembles](https://mlsanity.com/paper/1905.04194/) (2019)
- [Hierarchical Routing Mixture of Experts](https://mlsanity.com/paper/1903.07756/) (2019)

## Built on by (most cited first, 12 of 12)

- [Verifying Learning-Based Robotic Navigation Systems](https://mlsanity.com/paper/2205.13536/) (2022)
- [Iterative Bounding MDPs: Learning Interpretable Policies via Non-Interpretable Methods](https://mlsanity.com/paper/2102.13045/) (2021)
- [Verification-Guided Shielding for Deep Reinforcement Learning](https://mlsanity.com/paper/2406.06507/) (2024)
- [Learning Interpretable, High-Performing Policies for Autonomous Driving](https://mlsanity.com/paper/2202.02352/) (2022)
- [Verifying Generalization in Deep Learning](https://mlsanity.com/paper/2302.05745/) (2023)
- [Explainability in Deep Reinforcement Learning, a Review into Current Methods and Applications](https://mlsanity.com/paper/2207.01911/) (2022)
- [In Search of netUnicorn: A Data-Collection Platform to Develop Generalizable ML Models for Network Security Problems](https://mlsanity.com/paper/2306.08853/) (2023)
- [SkillTree: Explainable Skill-Based Deep Reinforcement Learning for Long-Horizon Control Tasks](https://mlsanity.com/paper/2411.12173/) (2024)
- [Verifying the Generalization of Deep Learning to Out-of-Distribution Domains](https://mlsanity.com/paper/2406.02024/) (2024)
- [Fidelity-Induced Interpretable Policy Extraction for Reinforcement Learning](https://mlsanity.com/paper/2309.06097/) (2023)
- [Robust Exploration in Directed Controller Synthesis via Reinforcement Learning with Soft Mixture-of-Experts](https://mlsanity.com/paper/2602.19244/) (2026)
- [REALM: Regime-Switching, Explainable, and Activation-Induced Linear Models](https://mlsanity.com/paper/2609.32141/) (2026)

## Abstract (arXiv)

Rapid advancements in deep learning have led to many recent breakthroughs. While deep learning models achieve superior performance, often statistically better than humans, their adoption into safety-critical settings, such as healthcare or self-driving cars is hindered by their inability to provide safety guarantees or to expose the inner workings of the model in a human understandable form. We present Mo"ET, a novel model based on Mixture of Experts, consisting of decision tree experts and a generalized linear model gating function. Thanks to such gating function the model is more expressive than the standard decision tree. To support non-differentiable decision trees as experts, we formulate a novel training procedure. In addition, we introduce a hard thresholding version, Mo"ETH, in which predictions are made solely by a single expert chosen via the gating function. Thanks to that property, Mo"ETH allows each prediction to be easily decomposed into a set of logical rules in a form which can be easily verified. While Mo"ET is a general use model, we illustrate its power in the reinforcement learning setting. By training Mo"ET models using an imitation learning procedure on deep RL agents we outperform the previous state-of-the-art technique based on decision trees while preserving the verifiability of the models. Moreover, we show that Mo"ET can also be used in real-world supervised problems on which it outperforms other verifiable machine learning models.