  We study the problem of constrained efficient global optimization, where both
the objective and constraints are expensive black-box functions that can be
learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient
Global Optimization), a simple and effective algorithm to solve it. Under
certain regularity assumptions, we show that our algorithm enjoys the same
cumulative regret bound as that in the unconstrained case and similar
cumulative constraint violation upper bounds. For commonly used Matern and
Squared Exponential kernels, our bounds are sublinear and allow us to derive a
convergence rate to the optimal solution of the original constrained problem.
In addition, our method naturally provides a scheme to declare infeasibility
when the original black-box optimization problem is infeasible. Numerical
experiments on sampled instances from the Gaussian process, artificial
numerical problems, and a black-box building controller tuning problem all
demonstrate the competitive performance of our algorithm. Compared to the other
state-of-the-art methods, our algorithm significantly improves the theoretical
guarantees, while achieving competitive empirical performance.
