论文标题
贝叶斯优化风险措施
Bayesian Optimization of Risk Measures
论文作者
论文摘要
我们考虑对$ρ[f（x，w）] $的目标功能的贝叶斯优化，其中$ f $是一个黑盒昂贵的评估功能，$ρ$表示VAR或CVAR风险度量，该量相对于环境随机变量$ W $所引起的随机性计算。这些问题在不确定性下的决策中出现，例如投资组合优化和健壮的系统设计。我们提出了一种新型的贝叶斯优化算法，该算法利用了目标函数的结构，以实质上提高采样效率。这些算法模型$ f $作为高斯过程，而不是直接对目标函数进行建模，而是在目标函数上使用隐含的后验来决定要评估哪些点。我们证明了我们在各种数值实验中的有效性。
We consider Bayesian optimization of objective functions of the form $ρ[ F(x, W) ]$, where $F$ is a black-box expensive-to-evaluate function and $ρ$ denotes either the VaR or CVaR risk measure, computed with respect to the randomness induced by the environmental random variable $W$. Such problems arise in decision making under uncertainty, such as in portfolio optimization and robust systems design. We propose a family of novel Bayesian optimization algorithms that exploit the structure of the objective function to substantially improve sampling efficiency. Instead of modeling the objective function directly as is typical in Bayesian optimization, these algorithms model $F$ as a Gaussian process, and use the implied posterior on the objective function to decide which points to evaluate. We demonstrate the effectiveness of our approach in a variety of numerical experiments.
