# Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks

arXiv: https://arxiv.org/abs/2602.09181 · HTML: https://mlsanity.com/paper/2602.09181/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 21 of 21)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models](https://mlsanity.com/paper/2311.11003/) (2023)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [Convergence of flow-based generative models via proximal gradient descent in Wasserstein space](https://mlsanity.com/paper/2310.17582/) (2023)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Practical Transfer Learning for Bayesian Optimization](https://mlsanity.com/paper/1802.02219/) (2018)
- [Transfer Learning with Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2111.11223/) (2021)
- [Self-Correcting Bayesian Optimization through Bayesian Active Learning](https://mlsanity.com/paper/2304.11005/) (2023)
- [Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes](https://mlsanity.com/paper/1801.01990/) (2018)
- [Multi-Fidelity Bayesian Optimization with Unreliable Information Sources](https://mlsanity.com/paper/2210.13937/) (2022)
- [Fair and Green Hyperparameter Optimization via Multi-objective and Multiple Information Source Bayesian Optimization](https://mlsanity.com/paper/2205.08835/) (2022)
- [We Still Don't Understand High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2512.00170/) (2025)
- [Time-Varying Gaussian Process Bandits with Unknown Prior](https://mlsanity.com/paper/2402.01632/) (2024)
- [Collaborative and Distributed Bayesian Optimization via Consensus: Showcasing the Power of Collaboration for Optimal Design](https://mlsanity.com/paper/2306.14348/) (2023)
- [Scalable Bayesian Optimization via Focalized Sparse Gaussian Processes](https://mlsanity.com/paper/2412.20375/) (2024)
- [Analytical Benchmark Problems for Multifidelity Optimization Methods](https://mlsanity.com/paper/2204.07867/) (2022)
- [Collaborative Bayesian Optimization via Wasserstein Barycenters](https://mlsanity.com/paper/2504.10770/) (2025)
- [Collaborative and Federated Black-box Optimization: A Bayesian Optimization Perspective](https://mlsanity.com/paper/2411.07523/) (2024)
- [Wasserstein Barycenter Gaussian Process based Bayesian Optimization](https://mlsanity.com/paper/2505.12471/) (2025)

## Abstract (arXiv)

Exploiting the analogy between Gaussian Distributions and Gaussian Processes' posterior, we present how the weighted Wasserstein Barycenter of Gaussian Processes (W2BGP) can be used to unify, under a common framework, different exotic Bayesian Optimization (BO) tasks. Specifically, collaborative/federated BO, (synchronous) batch BO, and multi-fidelity BO are considered in this paper. Our empirical analysis proves that each one of these tasks requires just an appropriate weighting schema for the W2BGP, while the entire framework remains untouched. Moreover, we demonstrate that the most well-known BO acquisition functions can be easily re-interpreted under the proposed framework and also enable a more computationally efficient way to deal with the computation of the Wasserstein Barycenter, compared with state-of-the-art methods from the Machine Learning literature. Finally, research perspectives branching from the proposed approach are presented.