  Unknown constraints arise in many types of expensive black-box optimization
problems. Several methods have been proposed recently for performing Bayesian
optimization with constraints, based on the expected improvement (EI)
heuristic. However, EI can lead to pathologies when used with constraints. For
example, in the case of decoupled constraints---i.e., when one can
independently evaluate the objective or the constraints---EI can encounter a
pathology that prevents exploration. Additionally, computing EI requires a
current best solution, which may not exist if none of the data collected so far
satisfy the constraints. By contrast, information-based approaches do not
suffer from these failure modes. In this paper, we present a new
information-based method called Predictive Entropy Search with Constraints
(PESC). We analyze the performance of PESC and show that it compares favorably
to EI-based approaches on synthetic and benchmark problems, as well as several
real-world examples. We demonstrate that PESC is an effective algorithm that
provides a promising direction towards a unified solution for constrained
Bayesian optimization.
