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.

我们研究高维和非稳态情景下的贝叶斯优化。我们提出了一个名为BALLET的框架，通过自适应过滤高置信度感兴趣区域（ROI）来解决现有算法在这些情景中通常需要大量超参数调整的问题。我们的方法易于调整，并能够聚焦于可以应用现有贝叶斯优化方法处理的优化空间的局部区域。关键思想是使用两个概率模型：一个粗糙的高斯过程（GP）用于识别ROI，一个局部化的GP用于ROI内的优化。我们理论上证明了BALLET可以有效缩小搜索空间，并且能够比没有ROI过滤的标准贝叶斯优化展现更紧的遗憾界限。我们通过合成和实际优化任务的实证研究证明了BALLET的有效性。

自适应水平集估计的贝叶斯优化感兴趣区域学习