论文标题
在不确定性下贝叶斯优化中的均值变化分析
Mean-Variance Analysis in Bayesian Optimization under Uncertainty
论文作者
论文摘要
我们考虑在不确定的环境中进行积极学习（AL），在这种环境中，需要考虑多种风险措施之间的权衡。作为在如此不确定的环境中的一个问题，我们研究了贝叶斯优化（MVA-BO）设置中的均值变化分析。均值变化分析是在金融工程领域开发的，并已用于做出决定，以考虑投资不确定性的平均值和差异之间的权衡。在本文中，我们专门针对BO设置不确定的组件，并考虑多任务，多目标和受约束的优化方案，以实现不确定组件的均值差异权衡。当目标黑框函数通过高斯过程（GP）建模时，我们得出了两种风险度量的界限，并根据风险度量范围为上述三个问题提出了AL算法。我们通过理论分析和数值实验显示了所提出的AL算法的有效性。
We consider active learning (AL) in an uncertain environment in which trade-off between multiple risk measures need to be considered. As an AL problem in such an uncertain environment, we study Mean-Variance Analysis in Bayesian Optimization (MVA-BO) setting. Mean-variance analysis was developed in the field of financial engineering and has been used to make decisions that take into account the trade-off between the average and variance of investment uncertainty. In this paper, we specifically focus on BO setting with an uncertain component and consider multi-task, multi-objective, and constrained optimization scenarios for the mean-variance trade-off of the uncertain component. When the target blackbox function is modeled by Gaussian Process (GP), we derive the bounds of the two risk measures and propose AL algorithm for each of the above three problems based on the risk measure bounds. We show the effectiveness of the proposed AL algorithms through theoretical analysis and numerical experiments.
