# Wasserstein Barycenter Gaussian Process based Bayesian Optimization

arXiv: https://arxiv.org/abs/2505.12471 · HTML: https://mlsanity.com/paper/2505.12471/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 18 May 2025.

## Builds on (most cited first, 16 of 16)

- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [No-Regret Bayesian Optimization with Unknown Hyperparameters](https://mlsanity.com/paper/1901.03357/) (2019)
- [Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation](https://mlsanity.com/paper/1911.12809/) (2019)
- [Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters](https://mlsanity.com/paper/1406.7758/) (2014)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Randomised Gaussian Process Upper Confidence Bound for Bayesian Optimisation](https://mlsanity.com/paper/2006.04296/) (2020)
- [Self-Correcting Bayesian Optimization through Bayesian Active Learning](https://mlsanity.com/paper/2304.11005/) (2023)
- [Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed](https://mlsanity.com/paper/2203.09179/) (2022)
- [Fair and Green Hyperparameter Optimization via Multi-objective and Multiple Information Source Bayesian Optimization](https://mlsanity.com/paper/2205.08835/) (2022)
- [PI is back! Switching Acquisition Functions in Bayesian Optimization](https://mlsanity.com/paper/2211.01455/) (2022)
- [Advancing Bayesian Optimization: The Mixed-Global-Local (MGL) Kernel and Length-Scale Cool Down](https://mlsanity.com/paper/1612.03117/) (2016)
- [SigOpt Mulch: An Intelligent System for AutoML of Gradient Boosted Trees](https://mlsanity.com/paper/2307.04849/) (2023)

## Built on by (most cited first, 2 of 2)

- [Gromov-Wasserstein and optimal transport: from assignment problems to probabilistic numeric](https://mlsanity.com/paper/2509.04089/) (2025)
- [Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks](https://mlsanity.com/paper/2602.09181/) (2026)

## Abstract (arXiv)

Gaussian Process based Bayesian Optimization is a widely applied algorithm to learn and optimize under uncertainty, well-known for its sample efficiency. However, recently -- and more frequently -- research studies have empirically demonstrated that the Gaussian Process fitting procedure at its core could be its most relevant weakness. Fitting a Gaussian Process means tuning its kernel's hyperparameters to a set of observations, but the common Maximum Likelihood Estimation technique, usually appropriate for learning tasks, has shown different criticalities in Bayesian Optimization, making theoretical analysis of this algorithm an open challenge. Exploiting the analogy between Gaussian Processes and Gaussian Distributions, we present a new approach which uses a prefixed set of hyperparameters values to fit as many Gaussian Processes and then combines them into a unique model as a Wasserstein Barycenter of Gaussian Processes. We considered both "easy" test problems and others known to undermine the textitvanilla Bayesian Optimization algorithm. The new method, namely Wasserstein Barycenter Gausssian Process based Bayesian Optimization (WBGP-BO), resulted promising and able to converge to the optimum, contrary to vanilla Bayesian Optimization, also on the most "tricky" test problems.