Constrained Bayesian Optimization with Max-Value Entropy Search
This work addresses constrained Bayesian optimization for real-world applications like hyperparameter tuning, but it is incremental as it builds on existing entropy search methods.
The authors tackled the problem of optimizing expensive black-box functions under unknown constraints, such as memory limits in deep neural network hyperparameter tuning, by proposing constrained Max-value Entropy Search (cMES), which outperformed prior methods on real-world problems with simpler implementation and faster computation.
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.