# Advancing Bayesian Optimization: The Mixed-Global-Local (MGL) Kernel and Length-Scale Cool Down

arXiv: https://arxiv.org/abs/1612.03117 · HTML: https://mlsanity.com/paper/1612.03117/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2016.

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

- [PFNs4BO: In-Context Learning for Bayesian Optimization](https://mlsanity.com/paper/2305.17535/) (2023)
- [Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimation](https://mlsanity.com/paper/2307.13371/) (2023)
- [LABCAT: Locally adaptive Bayesian optimization using principal-component-aligned trust regions](https://mlsanity.com/paper/2311.11328/) (2023)
- [Wasserstein Barycenter Gaussian Process based Bayesian Optimization](https://mlsanity.com/paper/2505.12471/) (2025)
- [Optimal Transport-based Permutation-Invariant Bayesian Optimization of Offshore Wind Farm Layouts](https://mlsanity.com/paper/2606.00009/) (2026)

## Abstract (arXiv)

Bayesian Optimization (BO) has become a core method for solving expensive black-box optimization problems. While much research focussed on the choice of the acquisition function, we focus on online length-scale adaption and the choice of kernel function. Instead of choosing hyperparameters in view of maximum likelihood on past data, we propose to use the acquisition function to decide on hyperparameter adaptation more robustly and in view of the future optimization progress. Further, we propose a particular kernel function that includes non-stationarity and local anisotropy and thereby implicitly integrates the efficiency of local convex optimization with global Bayesian optimization. Comparisons to state-of-the art BO methods underline the efficiency of these mechanisms on global optimization benchmarks.