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.
The BOCK algorithm of Oh et al. REF uses a cylindrical transformation of the search space to achieve scalability to high dimensions.
BOCK : Bayesian Optimization with Cylindrical Kernels
Proceedings of the 35th International Conference on Machine Learning, Stockholm, Sweden, PMLR 80, 2018
Mathematics Computer Science