论文标题
使用极值理论对随机系统进行可扩展风险分析
Toward Scalable Risk Analysis for Stochastic Systems Using Extreme Value Theory
论文作者
论文摘要
我们旨在分析有限时间随机系统的行为，该系统在更罕见和有害的结果的背景下，该系统无法获得模型。由于其稀有性，标准估计器无效地预测了此类结果。取而代之的是，我们使用极值理论（EVT），这是随机变量归一化最大值的长期行为的理论。我们使用上比较的$ρ（y）= e（\ max \ {y -μ，0 \}）$量化风险，该$ = e（y）$，$ y $ at landy变量$ y $。 $ρ（y）$是常见的均值 - upper-epemeviation juartional $μ+λρ（y）$，$λ\ in [0,1] $的风险部分。为了评估更罕见和有害的结果，我们在最坏情况的给定部分中提出了一个基于EVT的估计器，以$ρ（y）$。我们表明，根据流行的条件价值功能，我们的估计器具有封闭形式的表示。在实验中，我们使用少数I.I.D.估算器的外推能力说明了估计器的外推能力。样品（$ <$ 50）。当模型无法访问时，我们的方法对于估计有限时间系统的风险非常有用，并且数据收集昂贵。数值复杂性不会随状态空间的大小而增长。
We aim to analyze the behaviour of a finite-time stochastic system, whose model is not available, in the context of more rare and harmful outcomes. Standard estimators are not effective in making predictions about such outcomes due to their rarity. Instead, we use Extreme Value Theory (EVT), the theory of the long-term behaviour of normalized maxima of random variables. We quantify risk using the upper-semideviation $ρ(Y) = E(\max\{Y - μ,0\})$ of an integrable random variable $Y$ with mean $μ= E(Y)$. $ρ(Y)$ is the risk-aware part of the common mean-upper-semideviation functional $μ+ λρ(Y)$ with $λ\in [0,1]$. To assess more rare and harmful outcomes, we propose an EVT-based estimator for $ρ(Y)$ in a given fraction of the worst cases. We show that our estimator enjoys a closed-form representation in terms of the popular conditional value-at-risk functional. In experiments, we illustrate the extrapolation power of our estimator using a small number of i.i.d. samples ($<$50). Our approach is useful for estimating the risk of finite-time systems when models are inaccessible and data collection is expensive. The numerical complexity does not grow with the size of the state space.
