  We study Bayesian optimization (BO) in high-dimensional and non-stationary
scenarios. Existing algorithms for such scenarios typically require extensive
hyperparameter tuning, which limits their practical effectiveness. We propose a
framework, called BALLET, which adaptively filters for a high-confidence region
of interest (ROI) as a superlevel-set of a nonparametric probabilistic model
such as a Gaussian process (GP). Our approach is easy to tune, and is able to
focus on local region of the optimization space that can be tackled by existing
BO methods. The key idea is to use two probabilistic models: a coarse GP to
identify the ROI, and a localized GP for optimization within the ROI. We show
theoretically that BALLET can efficiently shrink the search space, and can
exhibit a tighter regret bound than standard BO without ROI filtering. We
demonstrate empirically the effectiveness of BALLET on both synthetic and
real-world optimization tasks.

Machine Learning;Machine Learning