Bayesian Optimization (BO) is used to find the global optima of black box functions. In this work, we propose a practical BO method of function compositions where the form of the composition is known but the constituent functions are expensive to evaluate. By assuming an independent Gaussian process (GP) model for each of the constituent black-box function, we propose Expected Improvement (EI) and Upper Confidence Bound (UCB) based BO algorithms and demonstrate their ability to outperform not just vanilla BO but also the current state-of-art algorithms. We demonstrate a novel application of the proposed methods to dynamic pricing in revenue management when the underlying demand function is expensive to evaluate.

翻译：贝叶斯优化（BO）常用于寻找黑箱函数的全局最优点。针对复合函数形式已知但各组成函数评估成本高昂的场景，本文提出一种实用的贝叶斯优化方法。通过为每个组成黑箱函数建立独立的高斯过程（GP）模型，我们提出了基于期望改进（EI）和置信上界（UCB）的BO算法，并验证了其在性能上不仅超越传统BO方法，更优于当前先进算法。本文进一步将该方法创新性地应用于收益管理中的动态定价问题，其中潜在需求函数的评估成本较高。