# Safe model-based Reinforcement Learning via Model Predictive Control and Control Barrier Functions

arXiv: https://arxiv.org/abs/2512.04856 · HTML: https://mlsanity.com/paper/2512.04856/

## Key facts

- Cited by 1 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 18 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## 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)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Data-driven Economic NMPC using Reinforcement Learning](https://mlsanity.com/paper/1904.04152/) (2019)
- [Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function](https://mlsanity.com/paper/2007.11718/) (2020)
- [Enhancing Feasibility and Safety of Nonlinear Model Predictive Control with Discrete-Time Control Barrier Functions](https://mlsanity.com/paper/2105.10596/) (2021)
- [Safety-Critical Control using Optimal-decay Control Barrier Function with Guaranteed Point-wise Feasibility](https://mlsanity.com/paper/2103.12375/) (2021)
- [On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach](https://mlsanity.com/paper/2305.03608/) (2023)
- [Reinforcement Learning with Model Predictive Control for Highway Ramp Metering](https://mlsanity.com/paper/2311.08820/) (2023)
- [When Do Transformers Outperform Feedforward and Recurrent Networks? A Statistical Perspective](https://mlsanity.com/paper/2503.11272/) (2025)

## Built on by (most cited first, 1 of 1)

- [Stable Transformer-Actor-Critic Model Predictive Control: A Contraction Analysis Approach](https://mlsanity.com/paper/2606.20197/) (2026)

## Abstract (arXiv)

Optimal control strategies are often combined with safety certificates to ensure both performance and safety in safety-critical systems. A prominent example is combining Model Predictive Control (MPC) with Control Barrier Functions (CBF). Yet, efficient tuning of MPC parameters and choosing an appropriate class K function in the CBF is challenging and problem dependent. This paper introduces a safe model-based Reinforcement Learning (RL) framework where a parametric MPC controller incorporates a CBF constraint with a parameterized class K function and serves as a function approximator to learn improved safe control policies from data. Three variations of the framework are introduced, distinguished by the way the optimization problem is formulated and the class K function is parameterized, including neural architectures. Numerical experiments on a discrete double-integrator with static and dynamic obstacles demonstrate that the proposed methods improve performance while ensuring safety.