  This paper presents a Bayesian optimization method with exponential
convergence without the need of auxiliary optimization and without the
delta-cover sampling. Most Bayesian optimization methods require auxiliary
optimization: an additional non-convex global optimization problem, which can
be time-consuming and hard to implement in practice. Also, the existing
Bayesian optimization method with exponential convergence requires access to
the delta-cover sampling, which was considered to be impractical. Our approach
eliminates both requirements and achieves an exponential convergence rate.
