Verifying the Effect of Initial Sample Size in Bayesian Optimization

Abstract

Obtaining the level of a factor that has the greatest effect on product development or crop cultivation is important given limited time, money, labor, and resources. Design of experiments is an approach to efficiently collect data in order to clarify the relationship between factors and effect. However, design of experiments mainly ends with the initial experimental design, which makes it difficult to conduct several more experiments based on the results. On the other hand, Bayesian Optimization, one of the methods of inverse estimation, uses Latin Hypercube design as the initial design of experiments and then conduct experiments sequentially. This is a powerful advantage of Bayesian Optimization.

Bayesian Optimization involves several factors including the kernel function, the acquisition function which evaluates experimental points, the initial design of experiments, and the total number of experiments. We clarify how many initial experimental points should be taken and whether the number of initial experimental points depends on the characteristics of the benchmark functions.

This research examines whether it is better to choose the optimal solution in Bayesian Optimization from the experimental points or from the mean value of the learned Gaussian Process Regression model. We provide guidance for users of Bayesian Optimization.