# Discontinuity-Sensitive Optimal Control Learning by Mixture of Experts

arXiv: https://arxiv.org/abs/1803.02493 · HTML: https://mlsanity.com/paper/1803.02493/

## Key facts

- Cited by 2 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 6 of its 26 references that are in the map.
- First posted on arXiv 7 Mar 2018.

## 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, 6 of 6)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Kinodynamic Motion Planning: A Novel Type Of Nonlinear, Passive Damping Forces And Advantages](https://mlsanity.com/paper/1606.09270/) (2016)
- [Learning the Problem-Optimum Map: Analysis and Application to Global Optimization in Robotics](https://mlsanity.com/paper/1605.04636/) (2016)

## Built on by (most cited first, 2 of 2)

- [Discrete State-Action Abstraction via the Successor Representation](https://mlsanity.com/paper/2206.03467/) (2022)
- [CoverLib: Classifiers-equipped Experience Library by Iterative Problem Distribution Coverage Maximization for Domain-tuned Motion Planning](https://mlsanity.com/paper/2405.02968/) (2024)

## Abstract (arXiv)

This paper proposes a discontinuity-sensitive approach to learn the solutions of parametric optimal control problems with high accuracy. Many tasks, ranging from model predictive control to reinforcement learning, may be solved by learning optimal solutions as a function of problem parameters. However, nonconvexity, discrete homotopy classes, and control switching cause discontinuity in the parameter-solution mapping, thus making learning difficult for traditional continuous function approximators. A mixture of experts (MoE) model composed of a classifier and several regressors is proposed to address such an issue. The optimal trajectories of different parameters are clustered such that in each cluster the trajectories are continuous function of problem parameters. Numerical examples on benchmark problems show that training the classifier and regressors individually outperforms joint training of MoE. With suitably chosen clusters, this approach not only achieves lower prediction error with less training data and fewer model parameters, but also leads to dramatic improvements in the reliability of trajectory tracking compared to traditional universal function approximation models (e.g., neural networks).