Uncertainty Quantification for Bayesian Optimization-猫眼课题宝

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2020-02

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Rui Tuo;Wenjia Wang

贝叶斯优化是一类全局优化技术。它把潜在的目标函数看作是一个高斯过程的实现。虽然根据高斯过程假设，贝叶斯优化的输出是随机的，但这种不确定性的量化在文献中很少研究。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，通过构造目标函数的最大值或最大值的置信度区域。这些区域可以高效地计算，并且它们的置信度由新开发的序贯高斯过程回归的统一误差界来保证。我们的理论为所有现有的序贯抽样策略和停止准则提供了一个统一的不确定性量化框架。

Bayesian optimization is a class of global optimization techniques. It regards the underlying objective function as a realization of a Gaussian process. Although the outputs of Bayesian optimization are random according to the Gaussian process assumption, 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, in terms of 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 newly developed uniform error bounds for sequential Gaussian process regression. Our theory provides a unified uncertainty quantification framework for all existing sequential sampling policies and stopping criteria.

Uncertainty Quantification for Bayesian Optimization

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