论文标题
贝叶斯优化的不确定性定量
Uncertainty Quantification for Bayesian Optimization
论文作者
论文摘要
贝叶斯优化是一类全球优化技术。在贝叶斯优化中，基础目标函数被建模为对高斯过程的实现。尽管高斯过程假设意味着贝叶斯优化输出的随机分布，但在文献中很少研究这种不确定性的量化。在这项工作中，我们提出了一种新的方法来评估贝叶斯优化算法的输出不确定性，该方法通过构建目标函数的最大点（或值）的置信区而进行。可以有效地计算这些区域，并通过在本工作中新开发的顺序高斯过程回归的均匀误差范围来保证它们的置信度。我们的理论为所有现有的顺序采样策略和停止标准提供了统一的不确定性量化框架。
Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random distribution of the Bayesian optimization outputs, quantification of this uncertainty is rarely studied in the literature. In this work, we propose a novel approach to assess the output uncertainty of Bayesian optimization algorithms, which proceeds by constructing confidence regions of the maximum point (or value) of the objective function. These regions can be computed efficiently, and their confidence levels are guaranteed by the uniform error bounds for sequential Gaussian process regression newly developed in the present work. Our theory provides a unified uncertainty quantification framework for all existing sequential sampling policies and stopping criteria.
