论文标题
最差的敏感性
Worst-case sensitivity
论文作者
论文摘要
我们介绍了最差的敏感性的概念，定义为当不确定性集的大小消失时，分布强劲优化的预期成本（DRO）模型的预期成本增加了。我们表明，最坏情况的敏感性是一种普遍的偏差度量，当不确定性集很小时，大量的DRO模型本质上是含义的（最坏情况）的灵敏度问题，统一了DRO和正常经验优化之间的关系的最新结果，具有较差的casase敏感性，可以发挥正常效果的作用。更一般而言，DRO溶液可以对不确定性集的家族和大小敏感，并反映其最坏情况的敏感性的特性。我们对众所周知的不确定性集的最差敏感性得出了封闭形式的表达，包括光滑的$ ϕ $ - 差异，总变化，“预算”的不确定性集，不确定性集，对应于期望值和CVAR的凸组合的不确定性集，以及Wasserstein Metric。这些可用于选择给定应用程序的不确定性集及其大小。
We introduce the notion of Worst-Case Sensitivity, defined as the worst-case rate of increase in the expected cost of a Distributionally Robust Optimization (DRO) model when the size of the uncertainty set vanishes. We show that worst-case sensitivity is a Generalized Measure of Deviation and that a large class of DRO models are essentially mean-(worst-case) sensitivity problems when uncertainty sets are small, unifying recent results on the relationship between DRO and regularized empirical optimization with worst-case sensitivity playing the role of the regularizer. More generally, DRO solutions can be sensitive to the family and size of the uncertainty set, and reflect the properties of its worst-case sensitivity. We derive closed-form expressions of worst-case sensitivity for well known uncertainty sets including smooth $ϕ$-divergence, total variation, "budgeted" uncertainty sets, uncertainty sets corresponding to a convex combination of expected value and CVaR, and the Wasserstein metric. These can be used to select the uncertainty set and its size for a given application.
