# Stability-informed Bayesian Optimization for MPC Cost Function Learning

arXiv: https://arxiv.org/abs/2404.12187 · HTML: https://mlsanity.com/paper/2404.12187/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 18 Apr 2024.

## Builds on (most cited first, 5 of 5)

- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [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)
- [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)

## Built on by (most cited first, 8 of 8)

- [Safe and Stable Closed-Loop Learning for Neural-Network-Supported Model Predictive Control](https://mlsanity.com/paper/2409.10171/) (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)
- [Model-free Reinforcement Learning for Model-based Control: Towards Safe, Interpretable and Sample-efficient Agents](https://mlsanity.com/paper/2507.13491/) (2025)
- [High-Dimensional Surrogate Modeling for Closed-Loop Learning of Neural-Network-Parameterized Model Predictive Control](https://mlsanity.com/paper/2512.11705/) (2025)
- [Hierarchical Decision Making with Structured Policies: A Principled Design via Inverse Optimization](https://mlsanity.com/paper/2606.28764/) (2026)

## Abstract (arXiv)

Designing predictive controllers towards optimal closed-loop performance while maintaining safety and stability is challenging. This work explores closed-loop learning for predictive control parameters under imperfect information while considering closed-loop stability. We employ constrained Bayesian optimization to learn a model predictive controller's (MPC) cost function parametrized as a feedforward neural network, optimizing closed-loop behavior as well as minimizing model-plant mismatch. Doing so offers a high degree of freedom and, thus, the opportunity for efficient and global optimization towards the desired and optimal closed-loop behavior. We extend this framework by stability constraints on the learned controller parameters, exploiting the optimal value function of the underlying MPC as a Lyapunov candidate. The effectiveness of the proposed approach is underlined in simulations, highlighting its performance and safety capabilities.