# Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learning

arXiv: https://arxiv.org/abs/2307.00828 · HTML: https://mlsanity.com/paper/2307.00828/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 53 references that are in the map.
- First posted on arXiv 3 Jul 2023.

## Builds on (most cited first, 30 of 34)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Sim-to-Real Transfer of Robotic Control with Dynamics Randomization](https://mlsanity.com/paper/1710.06537/) (2017)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Recasting Gradient-Based Meta-Learning as Hierarchical Bayes](https://mlsanity.com/paper/1801.08930/) (2018)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Trial without Error: Towards Safe Reinforcement Learning via Human Intervention](https://mlsanity.com/paper/1707.05173/) (2017)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Meta-Learning Priors for Efficient Online Bayesian Regression](https://mlsanity.com/paper/1807.08912/) (2018)
- [Cautious Adaptation For Reinforcement Learning in Safety-Critical Settings](https://mlsanity.com/paper/2008.06622/) (2020)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [Adaptive Safety with Control Barrier Functions](https://mlsanity.com/paper/1910.00555/) (2019)
- [Robust Regression for Safe Exploration in Control](https://mlsanity.com/paper/1906.05819/) (2019)
- [Meta-Learning Reliable Priors in the Function Space](https://mlsanity.com/paper/2106.03195/) (2021)
- [PAC-Bayes Control: Learning Policies that Provably Generalize to Novel Environments](https://mlsanity.com/paper/1806.04225/) (2018)
- [Probabilistic model predictive safety certification for learning-based control](https://mlsanity.com/paper/1906.10417/) (2019)
- [Bayesian Learning-Based Adaptive Control for Safety Critical Systems](https://mlsanity.com/paper/1910.02325/) (2019)
- [Safe Active Dynamics Learning and Control: A Sequential Exploration-Exploitation Framework](https://mlsanity.com/paper/2008.11700/) (2020)
- [Control Barriers in Bayesian Learning of System Dynamics](https://mlsanity.com/paper/2012.14964/) (2020)
- [Bayesian Multi-Task Learning MPC for Robotic Mobile Manipulation](https://mlsanity.com/paper/2211.10270/) (2022)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Online Control Barrier Functions for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2303.04313/) (2023)
- [Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments](https://mlsanity.com/paper/2201.01347/) (2022)
- [Provable Safe Reinforcement Learning with Binary Feedback](https://mlsanity.com/paper/2210.14492/) (2022)
- [Learning Control Barrier Functions with High Relative Degree for Safety-Critical Control](https://mlsanity.com/paper/2011.10721/) (2020)

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

- [Data-driven Control with Real-time Uncertainty Compensation for Multi-Fuel Engines](https://mlsanity.com/paper/2606.16171/) (2026)

## Abstract (arXiv)

Breaking safety constraints in control systems can lead to potential risks, resulting in unexpected costs or catastrophic damage. Nevertheless, uncertainty is ubiquitous, even among similar tasks. In this paper, we develop a novel adaptive safe control framework that integrates meta learning, Bayesian models, and control barrier function (CBF) method. Specifically, with the help of CBF method, we learn the inherent and external uncertainties by a unified adaptive Bayesian linear regression (ABLR) model, which consists of a forward neural network (NN) and a Bayesian output layer. Meta learning techniques are leveraged to pre-train the NN weights and priors of the ABLR model using data collected from historical similar tasks. For a new control task, we refine the meta-learned models using a few samples, and introduce pessimistic confidence bounds into CBF constraints to ensure safe control. Moreover, we provide theoretical criteria to guarantee probabilistic safety during the control processes. To validate our approach, we conduct comparative experiments in various obstacle avoidance scenarios. The results demonstrate that our algorithm significantly improves the Bayesian model-based CBF method, and is capable for efficient safe exploration even with multiple uncertain constraints.