  Many real-world optimisation problems such as hyperparameter tuning in
machine learning or simulation-based optimisation can be formulated as
expensive-to-evaluate black-box functions. A popular approach to tackle such
problems is Bayesian optimisation (BO), which builds a response surface model
based on the data collected so far, and uses the mean and uncertainty predicted
by the model to decide what information to collect next. In this paper, we
propose a novel variant of the well-known Knowledge Gradient acquisition
function that allows it to handle constraints. We empirically compare the new
algorithm with four other state-of-the-art constrained Bayesian optimisation
algorithms and demonstrate its superior performance. We also prove theoretical
convergence in the infinite budget limit.
