# Learning-based Model Predictive Control for Safe Exploration and Reinforcement Learning

arXiv: https://arxiv.org/abs/1906.12189 · HTML: https://mlsanity.com/paper/1906.12189/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2019.

## Built on by (most cited first, 16 of 16)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Conservative and Adaptive Penalty for Model-Based Safe Reinforcement Learning](https://mlsanity.com/paper/2112.07701/) (2021)
- [A safe exploration approach to constrained Markov decision processes](https://mlsanity.com/paper/2312.00561/) (2023)
- [Stability-Constrained Markov Decision Processes Using MPC](https://mlsanity.com/paper/2102.01383/) (2021)
- [Nested Mixture of Experts: Cooperative and Competitive Learning of Hybrid Dynamical System](https://mlsanity.com/paper/2011.10605/) (2020)
- [Safe Machine-Learning-supported Model Predictive Force and Motion Control in Robotics](https://mlsanity.com/paper/2303.04569/) (2023)
- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [Provably Optimal Reinforcement Learning under Safety Filtering](https://mlsanity.com/paper/2510.18082/) (2025)
- [Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes](https://mlsanity.com/paper/2108.06430/) (2021)
- [A Safety-Critical Decision Making and Control Framework Combining Machine Learning and Rule-based Algorithms](https://mlsanity.com/paper/2201.12819/) (2022)
- [Constrained Meta Reinforcement Learning with Provable Test-Time Safety](https://mlsanity.com/paper/2601.21845/) (2026)
- [Safely Learning Dynamical Systems](https://mlsanity.com/paper/2305.12284/) (2023)
- [Increasing Information for Model Predictive Control with Semi-Markov Decision Processes](https://mlsanity.com/paper/2501.17256/) (2025)
- [Hierarchical Reinforcement Learning with Low-Level MPC for Multi-Agent Control](https://mlsanity.com/paper/2509.15799/) (2025)
- [Safety Reinforced Model Predictive Control (SRMPC): Improving MPC with Reinforcement Learning for Motion Planning in Autonomous Driving](https://mlsanity.com/paper/2512.03774/) (2025)
- [When Can Safe Controllers Adapt? Information before Commitment](https://mlsanity.com/paper/2607.16895/) (2026)

## Abstract (arXiv)

Reinforcement learning has been successfully used to solve difficult tasks in complex unknown environments. However, these methods typically do not provide any safety guarantees during the learning process. This is particularly problematic, since reinforcement learning agent actively explore their environment. This prevents their use in safety-critical, real-world applications. In this paper, we present a learning-based model predictive control scheme that provides high-probability safety guarantees throughout the learning process. Based on a reliable statistical model, we construct provably accurate confidence intervals on predicted trajectories. Unlike previous approaches, we allow for input-dependent uncertainties. Based on these reliable predictions, we guarantee that trajectories satisfy safety constraints. Moreover, we use a terminal set constraint to recursively guarantee the existence of safe control actions at every iteration. We evaluate the resulting algorithm to safely explore the dynamics of an inverted pendulum and to solve a reinforcement learning task on a cart-pole system with safety constraints.