论文标题
基于CVAR的变分不平等的随机近似
Stochastic approximation of CVaR-based variational inequalities
论文作者
论文摘要
在本文中，我们研究了不确定功能的条件价值（CVAR）定义的变异不平等（VI）。我们介绍了随机近似方案，该方案在每次迭代时采用了CVAR的经验估计来解决这些VIS。我们研究了这些算法在各种假设下对VI的单调性和CVAR估计准确性的收敛。当CVAR的估计误差沿算法的任何执行逐渐较小时，我们的第一个算法显示会收敛到VI的精确解。当估计误差不变时，我们提供了两种算法，可证明可以收敛到VI解决方案的邻域。对于这些方案，在强大的单调性下，我们提供了样本量，估计误差和实现收敛的邻域大小之间的明确关系。一个模拟示例说明了我们的理论发现。
In this paper we study variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions. We introduce stochastic approximation schemes that employ an empirical estimate of the CVaR at each iteration to solve these VIs. We investigate convergence of these algorithms under various assumptions on the monotonicity of the VI and accuracy of the CVaR estimate. Our first algorithm is shown to converge to the exact solution of the VI when the estimation error of the CVaR becomes progressively smaller along any execution of the algorithm. When the estimation error is nonvanishing, we provide two algorithms that provably converge to a neighborhood of the solution of the VI. For these schemes, under strong monotonicity, we provide an explicit relationship between sample size, estimation error, and the size of the neighborhood to which convergence is achieved. A simulation example illustrates our theoretical findings.
