Bayesian optimization with partially specified queries

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

Automated summary

Bayesian optimization (BO) is a method for optimizing expensive and difficult-to-evaluate black-box functions, but specifying values for all input variables can be challenging. This paper introduces a new approach called Gaussian process bandit problem, BO with partially specified queries (BOPSQ), which allows for only some input variables to be specified. Algorithms based on posterior sampling are proposed for known and unknown input distributions, with demonstrated effectiveness on test functions and real-world datasets.