Exploring Exploration in Bayesian Optimization
This work provides a foundation for more principled design and analysis of acquisition functions in Bayesian optimization, addressing a key bottleneck for researchers and practitioners in optimization and machine learning.
The paper tackled the lack of quantitative measures for exploration in Bayesian optimization by introducing two novel approaches—observation traveling salesman distance and observation entropy—to quantify exploration characteristics of acquisition functions, revealing links between exploration and empirical performance across diverse black-box problems.
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.