  Bayesian optimization (BO) is a model-based approach to sequentially optimize
expensive black-box functions, such as the validation error of a deep neural
network with respect to its hyperparameters. In many real-world scenarios, the
optimization is further subject to a priori unknown constraints. For example,
training a deep network configuration may fail with an out-of-memory error when
the model is too large. In this work, we focus on a general formulation of
Gaussian process-based BO with continuous or binary constraints. We propose
constrained Max-value Entropy Search (cMES), a novel information
theoretic-based acquisition function implementing this formulation. We also
revisit the validity of the factorized approximation adopted for rapid
computation of the MES acquisition function, showing empirically that this
leads to inaccurate results. On an extensive set of real-world constrained
hyperparameter optimization problems we show that cMES compares favourably to
prior work, while being simpler to implement and faster than other constrained
extensions of Entropy Search.
