Reinforcement Learning Algorithms (RLA) are useful machine learning tools to understand how decision makers react to signals. It is known that RLA converge towards the pure Nash Equilibria (NE) of finite congestion games and more generally, finite potential games. For finite congestion games, only separable cost functions are considered. However, non-separable costs, which depend on the choices of all players instead of only those choosing the same resource, may be relevant in some circumstances, like in smart charging games. In this paper, finite congestion games with non-separable costs are shown to have an ordinal potential function, leading to the existence of an action-dependent continuous potential function. The convergence of a synchronous RLA towards the pure NE is then extended to this more general class of congestion games. Finally, a smart charging game is designed for illustrating convergence of such learning algorithms.

翻译：强化学习算术(RLA)是了解决策者如何对信号作出反应的有用的机器学习工具。 众所周知, RLA向有限的拥挤游戏和更一般而言的有限潜在游戏的纯Nash Equilibria(NE)汇合。 对于有限的拥挤游戏,只考虑可分离的成本功能。 但是,非分离成本(取决于所有玩家的选择,而不是仅取决于选择相同资源的人)在某些情况下可能具有相关性,例如在智能充电游戏中。 在本文中,带有不可分离成本的有限拥堵游戏被证明具有一个或正潜在功能,导致存在一个依赖行动的连续潜在功能。 同步的RLA与纯NE的趋同,然后扩大到这个更普遍的堵塞游戏类别。 最后, 智能充电游戏旨在说明这种学习算法的趋同。