Policy gradient methods enjoy strong practical performance in numerous tasks in reinforcement learning. Their theoretical understanding in multiagent settings, however, remains limited, especially beyond two-player competitive and potential Markov games. In this paper, we develop a new framework to characterize optimistic policy gradient methods in multi-player Markov games with a single controller. Specifically, under the further assumption that the game exhibits an equilibrium collapse, in that the marginals of coarse correlated equilibria (CCE) induce Nash equilibria (NE), we show convergence to stationary $\epsilon$-NE in $O(1/\epsilon^2)$ iterations, where $O(\cdot)$ suppresses polynomial factors in the natural parameters of the game. Such an equilibrium collapse is well-known to manifest itself in two-player zero-sum Markov games, but also occurs even in a class of multi-player Markov games with separable interactions, as established by recent work. As a result, we bypass known complexity barriers for computing stationary NE when either of our assumptions fails. Our approach relies on a natural generalization of the classical Minty property that we introduce, which we anticipate to have further applications beyond Markov games.

在这篇论文中，我们提出了一个新的框架来描述多人Markov游戏中的乐观策略梯度方法，在单个控制器下收敛到稳定的ε-NE，其收敛速度为O(1/ε^2)次迭代，该框架基于对经典Minty性质的自然推广，我们相信它在Markov游戏之外也有进一步的应用。

具有单一控制器的多人马尔可夫博弈中的乐观策略梯度：超越Minty属性的收敛