论文标题
基于CVAR的变异不平等的随机近似方法
Stochastic approximation approaches for CVaR-based variational inequalities
论文作者
论文摘要
本文考虑了不确定功能的条件值（CVAR）定义的变异不平等（VI），并提供了三个随机近似方案来解决它们。所有方法在每次迭代时使用CVAR的经验估计。第一种算法将迭代限制为使用投影的可行集。为了克服投影的计算负担，第二个处理不平等和平等约束，以不同的方式定义可行设置。特别是，通过使用惩罚函数来处理矩阵乘法和不等式来实现对相等限制定义的仿射子空间的投影。最后，第三个算法通过引入乘数更新完全丢弃了预测。我们建立了所有方案与VI解决方案的任何任意邻里的渐近融合。有关网络路由游戏的模拟示例说明了我们的理论发现。
This paper considers variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions and provides three stochastic approximation schemes to solve them. All methods use an empirical estimate of the CVaR at each iteration. The first algorithm constrains the iterates to the feasible set using projection. To overcome the computational burden of projections, the second one handles inequality and equality constraints defining the feasible set differently. Particularly, projection onto to the affine subspace defined by the equality constraints is achieved by matrix multiplication and inequalities are handled by using penalty functions. Finally, the third algorithm discards projections altogether by introducing multiplier updates. We establish asymptotic convergence of all our schemes to any arbitrary neighborhood of the solution of the VI. A simulation example concerning a network routing game illustrates our theoretical findings.
