  A major challenge in Bayesian Optimization is the boundary issue (Swersky,
2017) where an algorithm spends too many evaluations near the boundary of its
search space. In this paper, we propose BOCK, Bayesian Optimization with
Cylindrical Kernels, whose basic idea is to transform the ball geometry of the
search space using a cylindrical transformation. Because of the transformed
geometry, the Gaussian Process-based surrogate model spends less budget
searching near the boundary, while concentrating its efforts relatively more
near the center of the search region, where we expect the solution to be
located. We evaluate BOCK extensively, showing that it is not only more
accurate and efficient, but it also scales successfully to problems with a
dimensionality as high as 500. We show that the better accuracy and scalability
of BOCK even allows optimizing modestly sized neural network layers, as well as
neural network hyperparameters.
