Bayesian optimization with shape constraints

In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or more argument. We make the case that shape constraints are often appropriate in at least two important application areas of Bayesian optimization: (1) hyperparameter tuning of machine learning algorithms and (2) decision analysis with utility functions. We describe a methodology for incorporating a variety of shape constraints within the usual Bayesian optimization framework and present positive results from simple applications which suggest that Bayesian optimization with shape constraints is a promising topic for further research.