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Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks

arXiv 2602.09181 ↗First posted 9 Feb 2026cs.LGcited by 0

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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.

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References · 21

  1. 2019Scalable Global Optimization via Local Bayesian Optimizationcited by 359
  2. 2024Vanilla Bayesian Optimization Performs Great in High Dimensionscited by 87
  3. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  4. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Modelscited by 55
  5. 2018A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processescited by 52
  6. 2023Convergence of flow-based generative models via proximal gradient descent in Wasserstein spacecited by 34
  7. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  8. 2018Practical Transfer Learning for Bayesian Optimizationcited by 26
  9. 2021Transfer Learning with Gaussian Processes for Bayesian Optimizationcited by 26
  10. 2023Self-Correcting Bayesian Optimization through Bayesian Active Learningcited by 22
  11. 2018Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processescited by 19
  12. 2022Multi-Fidelity Bayesian Optimization with Unreliable Information Sourcescited by 17
9 more
  1. 2022Fair and Green Hyperparameter Optimization via Multi-objective and Multiple Information Source Bayesian Optimizationcited by 13
  2. 2024Time-Varying Gaussian Process Bandits with Unknown Priorcited by 10
  3. 2023Collaborative and Distributed Bayesian Optimization via Consensus: Showcasing the Power of Collaboration for Optimal Designcited by 9
  4. 2025We Still Don't Understand High-Dimensional Bayesian Optimizationcited by 9
  5. 2024Scalable Bayesian Optimization via Focalized Sparse Gaussian Processescited by 8
  6. 2022Analytical Benchmark Problems for Multifidelity Optimization Methodscited by 7
  7. 2025Collaborative Bayesian Optimization via Wasserstein Barycenterscited by 7
  8. 2024Collaborative and Federated Black-box Optimization: A Bayesian Optimization Perspectivecited by 5
  9. 2025Wasserstein Barycenter Gaussian Process based Bayesian Optimizationcited by 2

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