  The global optimization of a high-dimensional black-box function under
black-box constraints is a pervasive task in machine learning, control, and
engineering. These problems are challenging since the feasible set is typically
non-convex and hard to find, in addition to the curses of dimensionality and
the heterogeneity of the underlying functions. In particular, these
characteristics dramatically impact the performance of Bayesian optimization
methods, that otherwise have become the de facto standard for sample-efficient
optimization in unconstrained settings, leaving practitioners with evolutionary
strategies or heuristics. We propose the scalable constrained Bayesian
optimization (SCBO) algorithm that overcomes the above challenges and pushes
the applicability of Bayesian optimization far beyond the state-of-the-art. A
comprehensive experimental evaluation demonstrates that SCBO achieves excellent
results on a variety of benchmarks. To this end, we propose two new control
problems that we expect to be of independent value for the scientific
community.
