用加权沃瑟斯坦均值统一处理多种复杂贝叶斯优化任务
Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks
- 基于高斯过程后验与高斯分布的类比，提出加权沃瑟斯坦均值框架
- 不同任务仅需调整权重策略，无需修改整体框架，实验验证有效
- 可高效计算均值，且能重新解释主流采集函数，适合多场景优化
基于高斯分布与高斯过程后验之间的类比，本文提出加权沃瑟斯坦均值高斯过程（W2BGP）方法，用于在统一框架下处理多种异构贝叶斯优化（BO）任务。具体包括协同/联邦贝叶斯优化、批量（同步）贝叶斯优化以及多保真度贝叶斯优化。实证分析表明，各类任务仅需设计合适的权重方案即可适用该框架，而核心结构保持不变。此外，本文展示了最主流的贝叶斯优化采集函数可在新框架下被重新解释，并实现了比当前机器学习领域先进方法更高效的沃瑟斯坦均值计算。最后，论文还提出了由此方法延伸出的研究方向。
原文摘要 · Abstract (English)
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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