2023/12/19 by Ioannis Anagnostides, Ioannis Panageas, Anagnostides, Ioannis +5
Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Markov Chains and Monte Carlo Methods #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.2312.12067
openalex publication_date 2023/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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/ε2) iterations, where O(⋅) 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.