论文标题
使用内核平均嵌入在瞬间问题中的分布歧义下的最坏情况风险量化
Worst-Case Risk Quantification under Distributional Ambiguity using Kernel Mean Embedding in Moment Problem
论文作者
论文摘要
为了预测罕见和有影响力的事件，我们建议使用核心方法的最新发展（内核平均值嵌入）来量化分布歧义下的最坏情况。具体而言，我们提出了广义的力矩问题，其歧义集（即，矩约束）以非参数方式通过相关再现核希尔伯特空间的约束来描述。然后，我们提出可拖动的近似及其理论上的理由。作为具体应用，我们在数值上测试了提出的方法，以表征约束随机控制系统中最严重的约束违规概率。
In order to anticipate rare and impactful events, we propose to quantify the worst-case risk under distributional ambiguity using a recent development in kernel methods -- the kernel mean embedding. Specifically, we formulate the generalized moment problem whose ambiguity set (i.e., the moment constraint) is described by constraints in the associated reproducing kernel Hilbert space in a nonparametric manner. We then present the tractable approximation and its theoretical justification. As a concrete application, we numerically test the proposed method in characterizing the worst-case constraint violation probability in the context of a constrained stochastic control system.
