Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks

TL;DR

This paper introduces a unified framework using weighted Wasserstein Barycenter of Gaussian Processes to efficiently handle various exotic Bayesian Optimization tasks, simplifying computation and interpretation.

Contribution

The paper proposes a novel framework that unifies different exotic Bayesian Optimization tasks through weighted Wasserstein Barycenter of Gaussian Processes, enabling easier computation and reinterpretation of acquisition functions.

Findings

Framework effectively unifies multiple BO tasks with simple weighting schemes.

Reinterprets existing BO acquisition functions within the new framework.

Offers computational advantages over existing Wasserstein Barycenter methods.

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.