# An Analysis of Safety Guarantees in Multi-Task Bayesian Optimization

arXiv: https://arxiv.org/abs/2503.08555 · HTML: https://mlsanity.com/paper/2503.08555/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## 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)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [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)
- [On Safety in Safe Bayesian Optimization](https://mlsanity.com/paper/2403.12948/) (2024)
- [Towards Safe Multi-Task Bayesian Optimization](https://mlsanity.com/paper/2312.07281/) (2023)
- [Mean Square Prediction Error of Misspecified Gaussian Process Models](https://mlsanity.com/paper/1811.06642/) (2018)

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

- [Safe Bayesian Optimization for Uncertain Correlation Matrices in Linear Models of Co-Regionalization](https://mlsanity.com/paper/2605.13302/) (2026)

## Abstract (arXiv)

This paper addresses the integration of additional information sources into a Bayesian optimization framework while ensuring that safety constraints are satisfied. The interdependencies between these information sources are modeled using an unknown correlation matrix. We explore how uniform error bounds must be adjusted to maintain constraint satisfaction throughout the optimization process, considering both Bayesian and frequentist statistical perspectives. This is achieved by appropriately scaling the error bounds based on a confidence interval that can be estimated from the data. Furthermore, the efficacy of the proposed approach is demonstrated through experiments on two benchmark functions and a controller parameter optimization problem. Our results highlight a significant improvement in sample efficiency, demonstrating the methods suitability for optimizing expensive-to-evaluate functions.