Complex processes in science and engineering are often formulated as multistage decision-making problems. In this paper, we consider a type of multistage decision-making process called a cascade process. A cascade process is a multistage process in which the output of one stage is used as an input for the subsequent stage. When the cost of each stage is expensive, it is difficult to search for the optimal controllable parameters for each stage exhaustively. To address this problem, we formulate the optimization of the cascade process as an extension of the Bayesian optimization framework and propose two types of acquisition functions based on credible intervals and expected improvement. We investigate the theoretical properties of the proposed acquisition functions and demonstrate their effectiveness through numerical experiments. In addition, we consider an extension called suspension setting in which we are allowed to suspend the cascade process at the middle of the multistage decision-making process that often arises in practical problems. We apply the proposed method in a test problem involving a solar cell simulator, which was the motivation for this study.

翻译：科学与工程中的复杂过程常被建模为多阶段决策问题。本文研究一类被称为级联过程的多阶段决策过程。级联过程是一种多阶段过程，其中前一阶段的输出作为后续阶段的输入。当每个阶段的成本较高时，穷举搜索各阶段的最优可控参数变得困难。为解决此问题，我们将级联过程的优化问题建模为贝叶斯优化框架的扩展，并基于置信区间和期望改进提出两类采集函数。我们研究了所提采集函数的理论性质，并通过数值实验验证其有效性。此外，我们探讨了一种称为"暂停设置"的扩展场景——允许在多阶段决策过程中途暂停级联过程，该需求常见于实际问题中。我们将所提方法应用于本研究的动机问题：太阳能电池模拟器的测试问题。