Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimation
This addresses the issue of extensive hyperparameter tuning in existing Bayesian optimization methods for high-dimensional and non-stationary problems, offering a more practical solution.
The paper tackles the problem of Bayesian optimization in high-dimensional and non-stationary scenarios by proposing BALLET, a framework that adaptively filters for a region of interest to focus optimization, resulting in a tighter regret bound and demonstrated effectiveness on synthetic and real-world tasks.
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.