  Bayesian optimization (BO) is a global optimization strategy designed to find
the minimum of an expensive black-box function, typically defined on a compact
subset of $\mathcal{R}^d$, by using a Gaussian process (GP) as a surrogate
model for the objective. Although currently available acquisition functions
address this goal with different degree of success, an over-exploration effect
of the contour of the search space is typically observed. However, in problems
like the configuration of machine learning algorithms, the function domain is
conservatively large and with a high probability the global minimum does not
sit on the boundary of the domain. We propose a method to incorporate this
knowledge into the search process by adding virtual derivative observations in
the \gp at the boundary of the search space. We use the properties of GPs to
impose conditions on the partial derivatives of the objective. The method is
applicable with any acquisition function, it is easy to use and consistently
reduces the number of evaluations required to optimize the objective
irrespective of the acquisition used. We illustrate the benefits of our
approach in an extensive experimental comparison.
