# Safe and Stable Closed-Loop Learning for Neural-Network-Supported Model Predictive Control

arXiv: https://arxiv.org/abs/2409.10171 · HTML: https://mlsanity.com/paper/2409.10171/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Safe and constrained RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 16 Sep 2024.

## Placed in

- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 10 of 10)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Safe Reinforcement Learning Using Robust MPC](https://mlsanity.com/paper/1906.04005/) (2019)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processes](https://mlsanity.com/paper/1603.04915/) (2016)
- [Performance-oriented model learning for data-driven MPC design](https://mlsanity.com/paper/1904.10839/) (2019)
- [Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications](https://mlsanity.com/paper/2109.02606/) (2021)
- [Stability-informed Bayesian Optimization for MPC Cost Function Learning](https://mlsanity.com/paper/2404.12187/) (2024)
- [Safe Bayesian Optimization using Interior-Point Methods -- Applied to Personalized Insulin Dose Guidance](https://mlsanity.com/paper/2205.02327/) (2022)
- [Learning Model Predictive Control Parameters via Bayesian Optimization for Battery Fast Charging](https://mlsanity.com/paper/2404.06125/) (2024)

## Built on by (most cited first, 7 of 7)

- [Time-Series-Informed Closed-loop Learning for Sequential Decision Making and Control](https://mlsanity.com/paper/2412.02423/) (2024)
- [A Hierarchical Surrogate Model for Efficient Multi-Task Parameter Learning in Closed-Loop Control](https://mlsanity.com/paper/2508.12738/) (2025)
- [Exploiting Prior Knowledge in Preferential Learning of Individualized Autonomous Vehicle Driving Styles](https://mlsanity.com/paper/2503.15407/) (2025)
- [Efficient Controller Learning from Human Preferences and Numerical Data Via Multi-Modal Surrogate Models](https://mlsanity.com/paper/2603.24138/) (2026)
- [Safe Learning-Based Optimization of Model Predictive Control: Application to Battery Fast-Charging](https://mlsanity.com/paper/2410.04982/) (2024)
- [High-Dimensional Surrogate Modeling for Closed-Loop Learning of Neural-Network-Parameterized Model Predictive Control](https://mlsanity.com/paper/2512.11705/) (2025)
- [Exploiting Hierarchical Controller Structure in Contextual Parameter Learning for Humanoid Loco-Manipulation](https://mlsanity.com/paper/2610.04609/) (2026)

## Abstract (arXiv)

Safe learning of control policies remains challenging, both in optimal control and reinforcement learning. In this article, we consider safe learning of parametrized predictive controllers that operate with incomplete information about the underlying process. To this end, we employ Bayesian optimization for learning the best parameters from closed-loop data. Our method focuses on the system's overall long-term performance in closed-loop while keeping it safe and stable. Specifically, we parametrize the stage cost function of an MPC using a feedforward neural network. This allows for a high degree of flexibility, enabling the system to achieve a better closed-loop performance with respect to a superordinate measure. However, this flexibility also necessitates safety measures, especially with respect to closed-loop stability. To this end, we explicitly incorporated stability information in the Bayesian-optimization-based learning procedure, thereby achieving rigorous probabilistic safety guarantees. The proposed approach is illustrated using a numeric example.