Optimistic Policy Gradient in Multi-Player Markov Games with a Single Controller: Convergence Beyond the Minty Property
This work addresses theoretical gaps in reinforcement learning for multiagent systems, providing convergence guarantees in specific game classes, but it is incremental as it builds on known assumptions like equilibrium collapse.
The paper tackles the limited theoretical understanding of policy gradient methods in multiagent settings by developing a framework for optimistic policy gradient in multi-player Markov games with a single controller, showing convergence to stationary ε-Nash equilibria in O(1/ε²) iterations under an equilibrium collapse assumption.
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 $ε$-NE in $O(1/ε^2)$ 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.