# Towards Safe Multi-Task Bayesian Optimization

arXiv: https://arxiv.org/abs/2312.07281 · HTML: https://mlsanity.com/paper/2312.07281/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 12 Dec 2023.

## Builds on (most cited first, 11 of 11)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Safe Controller Optimization for Quadrotors with Gaussian Processes](https://mlsanity.com/paper/1509.01066/) (2015)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Bayesian Optimization for Policy Search via Online-Offline Experimentation](https://mlsanity.com/paper/1904.01049/) (2019)
- [Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications](https://mlsanity.com/paper/2109.02606/) (2021)
- [Efficient sample selection for safe learning](https://mlsanity.com/paper/2211.14104/) (2022)

## Built on by (most cited first, 5 of 5)

- [Towards safe Bayesian optimization with Wiener kernel regression](https://mlsanity.com/paper/2411.02253/) (2024)
- [(θl, θu)-Parametric Multi-Task Optimization: Joint Search in Solution and Infinite Task Spaces](https://mlsanity.com/paper/2503.08394/) (2025)
- [An Analysis of Safety Guarantees in Multi-Task Bayesian Optimization](https://mlsanity.com/paper/2503.08555/) (2025)
- [Offline Multi-Task Multi-Objective Data-Driven Evolutionary Algorithm with Language Surrogate Model and Implicit Q-Learning](https://mlsanity.com/paper/2512.15149/) (2025)
- [Safe Bayesian Optimization for Uncertain Correlation Matrices in Linear Models of Co-Regionalization](https://mlsanity.com/paper/2605.13302/) (2026)

## Abstract (arXiv)

Bayesian optimization has emerged as a highly effective tool for the safe online optimization of systems, due to its high sample efficiency and noise robustness. To further enhance its efficiency, reduced physical models of the system can be incorporated into the optimization process, accelerating it. These models are able to offer an approximation of the actual system, and evaluating them is significantly cheaper. The similarity between the model and reality is represented by additional hyperparameters, which are learned within the optimization process. Safety is a crucial criterion for online optimization methods such as Bayesian optimization, which has been addressed by recent works that provide safety guarantees under the assumption of known hyperparameters. In practice, however, this does not apply. Therefore, we extend the robust Gaussian process uniform error bounds to meet the multi-task setting, which involves the calculation of a confidence region from the hyperparameter posterior distribution utilizing Markov chain Monte Carlo methods. Subsequently, the robust safety bounds are employed to facilitate the safe optimization of the system, while incorporating measurements of the models. Simulation results indicate that the optimization can be significantly accelerated for expensive to evaluate functions in comparison to other state-of-the-art safe Bayesian optimization methods, contingent on the fidelity of the models.