# Learning-based Model Predictive Control for Safe Exploration

arXiv: https://arxiv.org/abs/1803.08287 · HTML: https://mlsanity.com/paper/1803.08287/

## Key facts

- Cited by 120 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2018.

## Built on by (most cited first, 30 of 120)

- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [Learning Policies with Zero or Bounded Constraint Violation for Constrained MDPs](https://mlsanity.com/paper/2106.02684/) (2021)
- [SafeVLA: Towards Safety Alignment of Vision-Language-Action Model via Constrained Learning](https://mlsanity.com/paper/2503.03480/) (2025)
- [Saute RL: Almost Surely Safe Reinforcement Learning Using State Augmentation](https://mlsanity.com/paper/2202.06558/) (2022)
- [Constrained Policy Optimization via Bayesian World Models](https://mlsanity.com/paper/2201.09802/) (2022)
- [SafeDreamer: Safe Reinforcement Learning with World Models](https://mlsanity.com/paper/2307.07176/) (2023)
- [Reinforcement Learning for Selective Key Applications in Power Systems: Recent Advances and Future Challenges](https://mlsanity.com/paper/2102.01168/) (2021)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Investigating Compounding Prediction Errors in Learned Dynamics Models](https://mlsanity.com/paper/2203.09637/) (2022)
- [Trustworthy Reinforcement Learning Against Intrinsic Vulnerabilities: Robustness, Safety, and Generalizability](https://mlsanity.com/paper/2209.08025/) (2022)
- [Safe Reinforcement Learning for Legged Locomotion](https://mlsanity.com/paper/2203.02638/) (2022)
- [Context-Aware Safe Reinforcement Learning for Non-Stationary Environments](https://mlsanity.com/paper/2101.00531/) (2021)
- [Model-based Constrained Reinforcement Learning using Generalized Control Barrier Function](https://mlsanity.com/paper/2103.01556/) (2021)
- [Sustainable Online Reinforcement Learning for Auto-bidding](https://mlsanity.com/paper/2210.07006/) (2022)
- [Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guarantees](https://mlsanity.com/paper/2201.08355/) (2022)
- [Stability Verification in Stochastic Control Systems via Neural Network Supermartingales](https://mlsanity.com/paper/2112.09495/) (2021)
- [Safe Reinforcement Learning Using Black-Box Reachability Analysis](https://mlsanity.com/paper/2204.07417/) (2022)
- [Learning Control Policies for Stochastic Systems with Reach-avoid Guarantees](https://mlsanity.com/paper/2210.05308/) (2022)
- [ActSafe: Active Exploration with Safety Constraints for Reinforcement Learning](https://mlsanity.com/paper/2410.09486/) (2024)
- [Balance Reward and Safety Optimization for Safe Reinforcement Learning: A Perspective of Gradient Manipulation](https://mlsanity.com/paper/2405.01677/) (2024)
- [Safe Reinforcement Learning with Chance-constrained Model Predictive Control](https://mlsanity.com/paper/2112.13941/) (2021)
- [CUP: A Conservative Update Policy Algorithm for Safe Reinforcement Learning](https://mlsanity.com/paper/2202.07565/) (2022)
- [Safe Continuous Control with Constrained Model-Based Policy Optimization](https://mlsanity.com/paper/2104.06922/) (2021)
- [Safe Reinforcement Learning of Dynamic High-Dimensional Robotic Tasks: Navigation, Manipulation, Interaction](https://mlsanity.com/paper/2209.13308/) (2022)
- [Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions](https://mlsanity.com/paper/2301.01526/) (2023)
- [A Human-Centered Safe Robot Reinforcement Learning Framework with Interactive Behaviors](https://mlsanity.com/paper/2302.13137/) (2023)
- [On Safety in Safe Bayesian Optimization](https://mlsanity.com/paper/2403.12948/) (2024)
- [Safe Reinforcement Learning on the Constraint Manifold: Theory and Applications](https://mlsanity.com/paper/2404.09080/) (2024)
- [Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach](https://mlsanity.com/paper/2104.09582/) (2021)
- [Compositional Policy Learning in Stochastic Control Systems with Formal Guarantees](https://mlsanity.com/paper/2312.01456/) (2023)

## Abstract (arXiv)

Learning-based methods have been successful in solving complex control tasks without significant prior knowledge about the system. However, these methods typically do not provide any safety guarantees, which prevents their use in safety-critical, real-world applications. In this paper, we present a learning-based model predictive control scheme that can provide provable high-probability safety guarantees. To this end, we exploit regularity assumptions on the dynamics in terms of a Gaussian process prior to construct provably accurate confidence intervals on predicted trajectories. Unlike previous approaches, we do not assume that model uncertainties are independent. Based on these 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. In our experiments, we show that the resulting algorithm can be used to safely and efficiently explore and learn about dynamic systems.