  Bayesian optimization has demonstrated impressive success in finding the
optimum input x* and output f* = f(x*) = max f(x) of a black-box function f. In
some applications, however, the optimum output f* is known in advance and the
goal is to find the corresponding optimum input x*. In this paper, we consider
a new setting in BO in which the knowledge of the optimum output f* is
available. Our goal is to exploit the knowledge about f* to search for the
input x* efficiently. To achieve this goal, we first transform the Gaussian
process surrogate using the information about the optimum output. Then, we
propose two acquisition functions, called confidence bound minimization and
expected regret minimization. We show that our approaches work intuitively and
give quantitatively better performance against standard BO methods. We
demonstrate real applications in tuning a deep reinforcement learning algorithm
on the CartPole problem and XGBoost on Skin Segmentation dataset in which the
optimum values are publicly available.
