Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks

2026-02-09

AI Summary

This work proposes a unified framework for efficiently addressing unconventional Bayesian optimization tasks, including collaborative/federated settings, synchronous batch evaluation, and multi-fidelity optimization. The core idea treats the Gaussian process posterior as a Gaussian distribution and introduces, for the first time, the weighted Wasserstein barycenter (W2BGP) to fuse information across tasks or sources. By designing task-specific weighting schemes, the framework adapts seamlessly to diverse optimization scenarios without altering its structural foundation—only the weights are adjusted. This approach not only yields novel interpretations of classical acquisition functions but also enhances computational efficiency. Empirical evaluations demonstrate that the method consistently outperforms existing approaches across multiple tasks, achieving both broad applicability and high efficiency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Bayesian Optimization
• Gaussian Processes
• Wasserstein Barycenter
• Federated Learning
• Multi-fidelity Optimization

Innovation

• Weighted Wasserstein Barycenter
• Gaussian Processes
• Bayesian Optimization
• Federated Learning
• Multi-fidelity Optimization