入力依存の分散を考慮したビジネス施策決定のためのベイズ最適化手法

In recent years, online shopping sites have implemented various business measures to improve profitability, including coupon issuance and point redemption. To optimize these measures and maximize profits, managers must set coupon discount amounts and point redemption amounts. One approach to solving this problem is to use machine learning to estimate a function with the inputs of business measures and the output of outcome variables. However, the relationship between the input and the output is not known in advance, and there is no training data for estimating the function before a measure is implemented. However, since the purpose of a business is to make a profit, it is often difficult to conduct large-scale experiments on real businesses where the only purpose is to acquire such data. On the other hand, Bayesian optimization is attracting attention as a method for performing sequential optimization of input while sequentially adding training data to an unknown function. Bayesian optimization estimates the posterior distribution of the output from the training data and uses an evaluation index called the acquisition function to estimate the next data point that will optimize the input. However, ordinary Bayesian optimization may not produce appropriate results when applied to practical business because it does not consider the characteristics of business effects, such as differences in variance depending on the input. Therefore, this study proposes a new acquisition function for Heteroskedastic Gaussian Process (hetGP), a function estimation method with different noise variances, that can consider the unique circumstances of business measures. This paper uses artificial data to demonstrate that the proposed method can effectively optimize business policies, even for functional data with input-dependent error variance that has not been handled by Bayesian optimization before. This method can enable regular optimization of business measures.