  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.
