We propose a multi-agent reinforcement learning dynamics, and analyze its convergence properties in infinite-horizon discounted Markov potential games. We focus on the independent and decentralized setting, where players can only observe the realized state and their own reward in every stage. Players do not have knowledge of the game model, and cannot coordinate with each other. In each stage of our learning dynamics, players update their estimate of a perturbed Q-function that evaluates their total contingent payoff based on the realized one-stage reward in an asynchronous manner. Then, players independently update their policies by incorporating a smoothed optimal one-stage deviation strategy based on the estimated Q-function. A key feature of the learning dynamics is that the Q-function estimates are updated at a faster timescale than the policies. We prove that the policies induced by our learning dynamics converge to a stationary Nash equilibrium in Markov potential games with probability 1. Our results build on the theory of two timescale asynchronous stochastic approximation, and new analysis on the monotonicity of potential function along the trajectory of policy updates in Markov potential games.

该论文提出了一种多智能体强化学习动态模型，分析了其在无限期贴现马尔可夫潜在博弈中的收敛性质。论文在独立和分散的环境下进行，重点研究了多智能体可以通过简单的学习动态方法在最小信息环境下达到马尔可夫潜在博弈的稳定纳什均衡。

马尔可夫潜在博弈中的独立和去中心化学习