Bayesian optimization with partially specified queries

Abstract Bayesian optimization (BO) is an approach to optimizing expensive-to-evaluate black-box function and sequentially determines the values of input variables evaluate function. However, it expensive in some cases becomes difficult specify for all variables, example, outsourcing scenarios where production queries with many involves significant cost. In this paper, we propose a novel Gaussian process bandit problem, BO partially specified (BOPSQ). BOPSQ, unlike standard setting, learner specifies only unspecified are randomly determined according known or unknown distribution. We two algorithms based on posterior sampling distributions. further derive their regret bounds that sublinear popular kernels. demonstrate effectiveness proposed using test functions real-world datasets.