Bayesian optimization is a technique for efficiently optimizing unknown functions in a black-box manner. To handle practical settings where gathering data requires use of finite resources, it is desirable to explicitly incorporate function evaluation costs into Bayesian optimization policies. To understand how to do so, we develop a previously-unexplored connection between cost-aware Bayesian optimization and the Pandora's Box problem, a decision problem from economics. The Pandora's Box problem admits a Bayesian-optimal solution based on an expression called the Gittins index, which can be reinterpreted as an acquisition function. We study the use of this acquisition function for cost-aware Bayesian optimization, and demonstrate empirically that it performs well, particularly in medium-high dimensions. We further show that this performance carries over to classical Bayesian optimization without explicit evaluation costs. Our work constitutes a first step towards integrating techniques from Gittins index theory into Bayesian optimization.

翻译：贝叶斯优化是一种以黑盒方式高效优化未知函数的技术。为应对实际场景中数据采集需消耗有限资源的情况，有必要将函数评估成本显式纳入贝叶斯优化策略。为探索实现路径，本研究首次建立了成本感知贝叶斯优化与经济学决策问题——潘多拉魔盒问题之间的理论关联。潘多拉魔盒问题存在一种基于吉廷斯指数表达式的贝叶斯最优解，该指数可重新阐释为采集函数。我们探究了该采集函数在成本感知贝叶斯优化中的应用，并通过实证证明其性能优异，尤其在中等至高维场景中表现突出。进一步研究表明，该优势同样适用于无显式评估成本的经典贝叶斯优化。本工作为将吉廷斯指数理论融入贝叶斯优化领域迈出了关键的第一步。