  Max-value entropy search (MES) is one of the state-of-the-art approaches in
Bayesian optimization (BO). In this paper, we propose a novel variant of MES
for constrained problems, called Constrained MES via Information lower BOund
(CMES-IBO), that is based on a Monte Carlo (MC) estimator of a lower bound of a
mutual information (MI). Unlike existing studies, our MI is defined so that
uncertainty with respect to feasibility can be incorporated. We derive a lower
bound of the MI that guarantees non-negativity, while a constrained counterpart
of conventional MES can be negative. We further provide theoretical analysis
that assures the low-variability of our estimator which has never been
investigated for any existing information-theoretic BO. Moreover, using the
conditional MI, we extend CMES-IBO to the parallel setting while maintaining
the desirable properties. We demonstrate the effectiveness of CMES-IBO by
several benchmark functions and real-world problems.
