Minimization of a class of rare event probabilities and buffered probabilities of exceedance
Minimization of a class of rare event probabilities and buffered probabilities of exceedance
复制标题
一类罕见事件概率和缓冲超越概率的最小化
DOI：
10.1007/s10479-021-03991-8
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发表时间：
2021
影响因子：
4.8
通讯作者：
Tran-Dinh, Quoc
中科院分区：
文献类型：
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作者：
Budhiraja, Amarjit;Lu, Shu;Yu, Yang;Tran-Dinh, Quoc
我们考虑的问题，选择设计参数，以尽量减少一个不希望的罕见的事件，通过ni.i.d.的平均描述的概率。随机变量由于接近最优设计参数的概率非常小，因此需要开发适当的加速蒙特-卡罗方法来估计其值。该研究中的挑战之一是，从被加数定律的指数扭曲进行模拟可能在计算上要求很高，因为这些转换后的定律可能是非标准的和难以处理的。我们考虑一个设置，其中的被加数是作为一个非线性函数的随机变量，其分布的指数扭曲采取一个简单的形式比原来的被加数。我们使用来自Dupuis和Wang（Stochastics 76（6）：481-508，2004，Math Oper Res 32（3）：723-757，2007）的技术来识别适当的Issacs方程，其子解用于构造易处理的重要性采样（IS）方案。我们还研究了密切相关的问题，估计缓冲概率的不确定性，并提供了第一个严格的结果，涉及缓冲概率的渐近性和普通概率下的大偏差标度。缓冲概率的类似最小化问题，在条件下，可以用凸优化问题来表示。我们表明，在条件下，渐近有效的措施（大偏差标度下）估计普通概率的变化也是渐近有效的估计缓冲概率。我们将构造的IS格式嵌入到梯度下降算法中来求解优化问题，并通过计算实验来说明这些方案。
We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average ofni.i.d. random variables. Since the probability of interest for near optimal design parameters is very small, one needs to develop suitable accelerated Monte-Carlo methods for estimating its value. One of the challenges in the study is that simulating from exponential twists of the laws of the summands may be computationally demanding since these transformed laws may be non-standard and intractable. We consider a setting where the summands are given as a nonlinear functional of random variables, the exponential twists of whose distributions take a simpler form than those for the original summands. We use techniques from Dupuis and Wang (Stochastics 76(6):481–508, 2004, Math Oper Res 32(3):723–757, 2007) to identify the appropriate Issacs equations whose subsolutions are used to construct tractable importance sampling (IS) schemes. We also study the closely related problem of estimating buffered probability of exceedance and provide the first rigorous results that relate the asymptotics of buffered probability and that of the ordinary probability under a large deviation scaling. The analogous minimization problem for buffered probability, under conditions, can be formulated as a convex optimization problem. We show that, under conditions, changes of measures that are asymptotically efficient (under the large deviation scaling) for estimating ordinary probability are also asymptotically efficient for estimating the buffered probability of exceedance. We embed the constructed IS scheme in gradient descent algorithms to solve the optimization problems, and illustrate these schemes through computational experiments.
数字通信中的重要性采样 - 第一部分：基础知识
DOI：
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发表时间：
1993
期刊：
IEEE J. Sel. Areas Commun.
影响因子：
--
作者：
Jyun;D. Lu;J. Sadowsky;K. Yao
通讯作者：
K. Yao
影响因子：
6.4
作者：
Mafusalov, Alexander;Shapiro, Alexander;Uryasev, Stan
通讯作者：
Uryasev, Stan
DOI：
--
发表时间：
1996
期刊：
影响因子：
--
作者：
J. Sadowsky
通讯作者：
J. Sadowsky