Constrained Bayesian optimization with max-value entropy search

Bayesian optimization (BO) is a model-based approach to minimize expensive black-boxes, and has been widely used to tune the hyperparameters of complex models such as deep neural networks. For many real-world black-boxes, however, the optimization is further subject to a priori unknown constraints. For example, model training may fail for certain configurations due to divergence or out of memory errors. To handle these failures, we focus on a general formulation of BO with binary feedback constraints. We propose constrained Max-Value Entropy Search (cMES), a novel information theoretic-based acquisition function implementing this formulation. We demonstrate that tuning the probability of constraint violation plays an important role, outperforming other commonly used heuristics. On an extensive set of real-world constrained hyperparameter optimization problems, we demonstrate that cMES compares favourably to prior work, while being simpler to implement and faster than other constrained extensions of entropy search.