Impact of invariant objective for order preserving transformation in Bayesian optimization
Shinichi Shirakawa · 2016
Bayesian optimization is a black-box optimization method, which maintains a surrogate model learned by using previously evaluated solutions and selects the next solution to be evaluated using the model. Since the Bayesian optimization method models the objective function as it is, it is not invariant under the order preserving transformation of the objective function. On the other hand, many evolutionary algorithms have that property only by using the ranking information of solutions. In this paper, we introduce two types of invariant objective function: the ranking-based objective and the Lebesgue measure-based objective, into the Bayesian optimization in order to realize the invariance property. The impact of the invariant objective function for the search performance is verified through the numerical experiment. The experimental result shows that the introduced objectives achieve the invariance for the order preserving transformation without the considerable performance deterioration in the Bayesian optimization.