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Bayesian optimization (BO) is a model-based approach to sequentially optimizeexpensive black-box functions, such as the validation error of a deep neuralnetwork with respect to its hyperparameters. In many real-world scenarios, theoptimization is further subject to a priori unknown constraints. For example,training a deep network configuration may fail with an out-of-memory error whenthe model is too large. In this work, we focus on a general formulation ofGaussian process-based BO with continuous or binary constraints. We proposeconstrained Max-value Entropy Search (cMES), a novel informationtheoretic-based acquisition function implementing this formulation. We alsorevisit the validity of the factorized approximation adopted for rapidcomputation of the MES acquisition function, showing empirically that thisleads to inaccurate results. On an extensive set of real-world constrainedhyperparameter optimization problems we show that cMES compares favourably toprior work, while being simpler to implement and faster than other constrainedextensions of Entropy Search.

Constrained Bayesian Optimization with Max-Value Entropy Search