学习线-水中平均田野游戏的探索噪音 (Exploration noise for learning linear-quadratic mean field games)

The goal of this paper is to demonstrate that common noise may serve as an exploration noise for learning the solution of a mean field game. This concept is here exemplified through a toy linear-quadratic model, for which a suitable form of common noise has already been proven to restore existence and uniqueness. We here go one step further and prove that the same form of common noise may force the convergence of the learning algorithm called `fictitious play', and this without any further potential or monotone structure. Several numerical examples are provided in order to support our theoretical analysis.

翻译：本文的目的是要表明,常见噪音可以作为一种探索噪音,用来学习一种中性野外游戏的解决方案。这个概念在这里通过玩具线性水面模型加以示范,对于这种模型,已经证明一种合适的常见噪音形式可以恢复存在和独特性。我们在此进一步证明,同样形式的常见噪音可能迫使称为“假玩”的学习算法趋同,而这种算法没有任何进一步的潜力或单调结构。为了支持我们的理论分析,提供了几个数字例子。