线性收敛速率的算法A：纳什均衡解搜索的分析

Theorem 1 demonstrates that algorithm A, when designed with a reasonable choice of fixed step size 'A' and tuning parameter 'B', will experience linear convergence rate. In addition, conditions for selecting effective values of 'A' and 'B' such that the spectral radius 'C' is less than 1 are provided in 'S' and 'D'. The impact of topological parameters 'E', problem-related parameters 'W', and the number of players 'Q' on parameter selection is also revealed. The results show that although the presence of uncertainty hinders the search for Nash equilibrium solutions, the error sequence 'S' will converge to 0 in the expected sense when the growth of the number of sampled pseudo-gradients satisfies 'A'.