Optimistic Policy Gradient in Multi-Player Markov Games with a Single Controller: Convergence Beyond the Minty Property

Ioannis Anagnostides, Ioannis Panageas, Gabriele Farina, Tuomas Sandholm

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Abstract

Policy gradient methods enjoy strong practical performance in numerous tasks in multiagent reinforcement learning. Their theoretical understanding, 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. 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. Our results 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.

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Bibtex entry

@inproceedings{Anagnostides24:Optimistic, title={Optimistic Policy Gradient in Multi-Player Markov Games with a Single Controller: Convergence Beyond the Minty Property}, author={Ioannis Anagnostides and Ioannis Panageas and Gabriele Farina and Tuomas Sandholm}, booktitle={AAAI Conference on Artificial Intelligence}, year={2024} }