量化贝叶斯优化中探索行为，揭示不同方法的优劣
Exploring Exploration in Bayesian Optimization
- 用旅行商距离和观察熵衡量探索程度
- 发现探索性与实际性能存在关联
- 为设计更优采集函数提供新思路
在贝叶斯优化中，探索与利用的平衡对采集函数的成功至关重要。然而，缺乏对探索行为的定量度量，导致难以分析和比较不同采集函数。本文提出两种新方法——观测旅行商距离和观测熵，基于所选观测点量化采集函数的探索特性。利用这些度量，我们在多种黑箱问题上分析了多个经典采集函数的探索性质，揭示了探索性与实际性能之间的联系，并发现了现有采集函数间的新关系。这些度量不仅深化了对采集函数的理解，也为更系统、更严谨地设计采集函数奠定了基础。
原文摘要 · Abstract (English)
A well-balanced exploration-exploitation trade-off is crucial for successful acquisition functions in Bayesian optimization. However, there is a lack of quantitative measures for exploration, making it difficult to analyze and compare different acquisition functions. This work introduces two novel approaches - observation traveling salesman distance and observation entropy - to quantify the exploration characteristics of acquisition functions based on their selected observations. Using these measures, we examine the explorative nature of several well-known acquisition functions across a diverse set of black-box problems, uncover links between exploration and empirical performance, and reveal new relationships among existing acquisition functions. Beyond enabling a deeper understanding of acquisition functions, these measures also provide a foundation for guiding their design in a more principled and systematic manner.
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