论文标题
随机广义NASH平衡问题的分布式投影反向梯度算法
Distributed projected-reflected-gradient algorithms for stochastic generalized Nash equilibrium problems
论文作者
论文摘要
我们考虑具有关节可行性限制和预期值成本函数的随机通用NASH平衡问题（SGNEP）。我们提出了一个分布式随机的投影反射梯度算法，并在伪映射映射是单调且溶液是唯一的时显示了其几乎确定的收敛性。该算法基于单调操作员分裂方法，该方法是针对SGNEPS量身定制的，当时在每次迭代中通过越来越多的随机变量样品近距离近似估计预期值映射。最后，我们表明，当伪映射映射具有碳化作用时，我们提出的算法的预处理可以保证。
We consider the stochastic generalized Nash equilibrium problem (SGNEP) with joint feasibility constraints and expected-value cost functions. We propose a distributed stochastic projected reflected gradient algorithm and show its almost sure convergence when the pseudogradient mapping is monotone and the solution is unique. The algorithm is based on monotone operator splitting methods tailored for SGNEPs when the expected-value pseudogradient mapping is approximated at each iteration via an increasing number of samples of the random variable. Finally, we show that a preconditioned variant of our proposed algorithm has convergence guarantees when the pseudogradient mapping is cocoercive.
