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.

翻译：我们研究了高维和非平稳场景下的贝叶斯优化（BO）。现有针对此类场景的算法通常需要大量的超参数调优，这限制了它们的实际有效性。我们提出一个名为BALLET的框架，该框架自适应地筛选出一个高置信度的感兴趣区域（ROI），作为非参数概率模型（如高斯过程（GP））的超水平集。我们的方法易于调优，并且能够聚焦于优化空间中可由现有BO方法处理的局部区域。其关键思想是使用两个概率模型：一个粗粒度GP用于识别ROI，以及一个局部化GP用于在ROI内进行优化。我们从理论上证明，BALLET能够有效缩小搜索空间，并且相比无ROI筛选的标准BO，能够展现出更紧致的遗憾界。我们通过合成和实际优化任务的实证结果，展示了BALLET的有效性。