论文标题
在本地耦合网络游戏中，分布式随机NASH平衡学习，参数未知
Distributed Stochastic Nash Equilibrium Learning in Locally Coupled Network Games with Unknown Parameters
论文作者
论文摘要
在随机的纳什均衡问题（SNEP）中，玩家对自己的复杂环境不确定并在模型中具有多维未知参数是很自然的。在各种SNEP中，本文着重于本地耦合的网络游戏，在这些网络游戏中，每个理性玩家的目标都受到其邻居的总影响。我们提出了一种基于近端迭代和普通最小二乘估计器的分布式学习算法，其中每个玩家反复更新相邻决策的本地估计值，这使得鉴于当前的估计参数获得了实现的目标值，并将其增强的最佳响应决策带来了未知的参数。利用Robbins-siegmund定理和M估计量的大偏差定律，我们确定了拟议算法几乎确定的融合到以适当速率更新步骤衰减时，拟议的算法与SNEP解决方案的收敛。
In stochastic Nash equilibrium problems (SNEPs), it is natural for players to be uncertain about their complex environments and have multi-dimensional unknown parameters in their models. Among various SNEPs, this paper focuses on locally coupled network games where the objective of each rational player is subject to the aggregate influence of its neighbors. We propose a distributed learning algorithm based on the proximal-point iteration and ordinary least-square estimator, where each player repeatedly updates the local estimates of neighboring decisions, makes its augmented best-response decisions given the current estimated parameters, receives the realized objective values, and learns the unknown parameters. Leveraging the Robbins-Siegmund theorem and the law of large deviations for M-estimators, we establish the almost sure convergence of the proposed algorithm to solutions of SNEPs when the updating step sizes decay at a proper rate.
