Multi-agent reinforcement learning has been successfully applied to fully-cooperative and fully-competitive environments, but little is currently known about mixed cooperative/competitive environments. In this paper, we focus on a particular class of multi-agent mixed cooperative/competitive stochastic games called Markov Potential Games (MPGs), which include cooperative games as a special case. Recent results have shown that independent policy gradient converges in MPGs but it was not known whether Independent Natural Policy Gradient converges in MPGs as well. We prove that Independent Natural Policy Gradient always converges in the last iterate using constant learning rates. The proof deviates from the existing approaches and the main challenge lies in the fact that Markov Potential Games do not have unique optimal values (as single-agent settings exhibit) so different initializations can lead to different limit point values. We complement our theoretical results with experiments that indicate that Natural Policy Gradient outperforms Policy Gradient in routing games and congestion games.

本文研究了多智能体协作/竞争情景下的马尔科夫潜在博弈（Markov Potential Games，简称MPGs），证明了独立自然策略梯度（Independent Natural Policy Gradient）在其内部一定会收敛，同时通过实验表明了自然策略梯度在路径游戏（routing games）和拥塞游戏（congestion games）中的优越性。

独立自然策略梯度总是收敛于马尔科夫潜在博弈