In multi-agent reinforcement learning (MARL), independent learners are those that do not access the action selections of other agents in the system. Due to the decentralization of information, it is generally difficult to design independent learners that drive the system to equilibrium. This paper investigates the feasibility of using \emph{satisficing} dynamics to guide independent learners to approximate equilibrium policies in non-episodic, discounted stochastic games. Satisficing refers to halting search in an optimization problem upon finding a satisfactory but possibly suboptimal input; here, we take it to mean halting search upon finding an input that achieves a cost within $\epsilon$ of the minimum cost. In this paper, we define a useful structural concept for games, to be termed the $\epsilon$-satisficing paths property, and we prove that this property holds for any $\epsilon \geq 0$ in general two-player stochastic games and in $N$-player stochastic games satisfying a symmetry condition. To illustrate the utility of this property, we present an independent learning algorithm that comes with high probability guarantees of approximate equilibrium in $N$-player symmetric games. This guarantee is made assuming symmetry alone, without additional assumptions such as a zero sum, team, or potential game structure. %

翻译：在多试剂强化学习(MARL)中,独立学习者是指那些无法进入系统中其他代理者的行动选择的学习者。由于信息分散化,通常很难设计能够使系统达到平衡的独立学习者。本文调查使用 emph{satisficting} 动态来指导独立学习者在非刺激、折扣的随机游戏中采用近似平衡政策的可行性。 满意是指在寻找满意但可能次优的游戏输入时停止搜索; 这里, 我们的意思是, 在找到一个在最低成本中以$\epslon计的成本达到成本的输入时, 停止搜索。 在本文中, 我们定义了一个有用的游戏结构概念, 称为 $\ epsilon- satisficational pathfical 属性, 并且我们证明, 在普通的两玩家随机游戏中, 和 $$$nn- player setectritical 游戏中, 我们独立地算出一种高概率的游戏结构的效用, 。