The existing stochastic approximation (SA)-type algorithms for two-stage stochastic variational inequalities (SVIs) are based on the uniqueness of the second-stage solution, which restricts the use of those algorithms. In this paper, we propose a dynamic sampling stochastic projection gradient method (DS-SPGM) for solving a class of two-stage SVIs satisfying the co-coercive property. With the co-coercive property and the dynamic sampling technique, we can handle the two-stage SVIs when the second-stage problem has multiple solutions and achieve the rate of convergence with \(\varvec{O}(\varvec{1/\sqrt{K}})\). Moreover, numerical experiments show the efficiency of the DS-SPGM.

现有的两阶段随机变分不等式（SVI）的随机近似（SA）型算法基于第二阶段解的唯一性，这限制了这些算法的使用。在本文中，我们提出了一种动态采样随机投影梯度法（DS-SPGM）来求解一类满足强制性质的两阶段SVI。利用强制性质和动态采样技术，当第二阶段问题有多个解时，我们可以处理两阶段SVI，并达到\(\varvec{O}(\varvec{1/\ sqrt{K}})\)。此外，数值实验显示了 DS-SPGM 的效率。