BOCK : Bayesian Optimization with Cylindrical Kernels

TL;DR

BOCK introduces a cylindrical kernel transformation in Bayesian Optimization to reduce boundary bias, improve accuracy, and scale efficiently to high-dimensional problems, including neural network hyperparameter tuning.

Contribution

The paper proposes BOCK, a novel Bayesian Optimization method using cylindrical kernels to address boundary issues and enhance scalability to high-dimensional spaces.

Findings

BOCK outperforms traditional methods in accuracy and efficiency.

BOCK scales to problems with up to 500 dimensions.

BOCK effectively optimizes neural network hyperparameters.

Abstract

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.