论文标题
基于随机近似的随机变异不平等现象
Stochastic Approximation Based Confidence Regions for Stochastic Variational Inequalities
论文作者
论文摘要
样本平均近似（SAA）和随机近似（SA）是解决随机变化不平等问题（SVIP）的两个流行方案。在过去的几十年中，已经对SAA解决方案和SA解决方案的一致性的理论进行了充分的研究。最近，在实施SAA方案时已经构建了真正解决SVIP的渐近置信区。当采用SA计划时，将真正解决方案的真正解决方案的信心区域开发为基本利益。在本文中，我们讨论了为SVIP的真实解决方案构建渐近置信区域的框架，重点是随机双平均方法。我们首先以奇异的意义和非共性意义上建立了SA解决方案的渐近正态性。然后研究了估计正常分布中协方差矩阵的在线方法。最后，提出了通过数值模拟建立SVIP解决方案的渐近置信区域的实际程序。
The sample average approximation (SAA) and the stochastic approximation (SA) are two popular schemes for solving the stochastic variational inequalities problem (SVIP). In the past decades, theories on the consistency of the SAA solutions and SA solutions have been well studied. More recently, the asymptotic confidence regions of the true solution to SVIP have been constructed when the SAA scheme is implemented. It is of fundamental interest to develop confidence regions of the true solution to the SVIP when the SA scheme is employed. In this paper, we discuss the framework of constructing asymptotic confidence regions for the true solution of SVIP with a focus on stochastic dual average method. We first establish the asymptotic normality of the SA solutions both in ergodic sense and non-ergodic sense. Then the online methods of estimating the covariance matrices in the normal distributions are studied. Finally, practical procedures of building the asymptotic confidence regions of solutions to SVIP with numerical simulations are presented.
