Bayesian Optimization for Cascade-type Multi-stage Processes

TL;DR

This paper extends Bayesian optimization to efficiently optimize complex multistage cascade processes with expensive stages, introducing new acquisition functions and a suspension setting, demonstrated on a solar cell simulator.

Contribution

It proposes novel Bayesian optimization methods tailored for cascade processes, including theoretical analysis and practical extension with suspension capability.

Findings

Effective optimization of cascade processes demonstrated in numerical experiments.

Proposed acquisition functions outperform traditional methods.

Extension with suspension setting improves flexibility in practical applications.

Abstract

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.