# Safe Bayesian Optimization for Uncertain Correlation Matrices in Linear Models of Co-Regionalization

arXiv: https://arxiv.org/abs/2605.13302 · HTML: https://mlsanity.com/paper/2605.13302/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 12 of 12)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Meta-Learning: A Survey](https://mlsanity.com/paper/1810.03548/) (2018)
- [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)
- [PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees](https://mlsanity.com/paper/2002.05551/) (2020)
- [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)
- [Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications](https://mlsanity.com/paper/2109.02606/) (2021)
- [Towards Safe Multi-Task Bayesian Optimization](https://mlsanity.com/paper/2312.07281/) (2023)
- [MALIBO: Meta-learning for Likelihood-free Bayesian Optimization](https://mlsanity.com/paper/2307.03565/) (2023)
- [Bayesian Optimization-based Nonlinear Adaptive PID Controller Design for Robust Mobile Manipulation](https://mlsanity.com/paper/2207.04866/) (2022)
- [An Analysis of Safety Guarantees in Multi-Task Bayesian Optimization](https://mlsanity.com/paper/2503.08555/) (2025)

## Abstract (arXiv)

This paper extends safety guarantees for multi-task Bayesian optimization with uncertain co-regionalization matrices from intrinsic co-regionalization models to linear models of co-regionalization. The latter allows for more flexible modeling of the inter-task correlations by composing multiple features. We derive uniform error bounds for vector-valued functions sampled from a Gaussian process with a linear model of co-regionalization kernel. Furthermore, we show the potential performance gains of linear models of co-regionalization in a numerical comparison on a safe multi-task Bayesian optimization benchmark.