  The optimization of expensive-to-evaluate black-box functions is prevalent in
various scientific disciplines. Bayesian optimization is an automatic, general
and sample-efficient method to solve these problems with minimal knowledge of
the underlying function dynamics. However, the ability of Bayesian optimization
to incorporate prior knowledge or beliefs about the function at hand in order
to accelerate the optimization is limited, which reduces its appeal for
knowledgeable practitioners with tight budgets. To allow domain experts to
customize the optimization routine, we propose ColaBO, the first
Bayesian-principled framework for incorporating prior beliefs beyond the
typical kernel structure, such as the likely location of the optimizer or the
optimal value. The generality of ColaBO makes it applicable across different
Monte Carlo acquisition functions and types of user beliefs. We empirically
demonstrate ColaBO's ability to substantially accelerate optimization when the
prior information is accurate, and to retain approximately default performance
when it is misleading.
