We consider the stochastic generalized Nash equilibrium problem (SGNEP) with joint feasibility constraints and expected-value cost functions. We propose a distributed stochastic preconditioned projected reflected gradient algorithm and show its almost sure convergence when the pseudogradient mapping is cocoercive. The algorithm is based on monotone operator splitting methods for SGNEPs when the expected-value pseudogradient mapping is approximated at each iteration via an increasing number of samples of the random variable, an approach known as sample average approximation. Finally, we show that a non-preconditioned variant of our proposed algorithm has less restrictive convergence guarantees than state-of-the-art (preconditioned) forward-backward algorithms.

中文翻译：

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随机广义纳什均衡问题的分布式（预处理）投影反射梯度算法

我们考虑具有联合可行性约束和期望值成本函数的随机广义纳什均衡问题 (SGNEP)。我们提出了一种分布式随机预条件投影反射梯度算法，并在伪梯度映射是强制性的时展示了其几乎肯定的收敛性。该算法基于 SGNEP 的单调算子分裂方法，当期望值伪梯度映射在每次迭代时通过增加随机变量的样本数量来近似，这种方法称为样本平均近似。最后，我们表明我们提出的算法的非预处理变体比最先进的（预处理的）前向后向算法具有更少的收敛保证。