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This research establishes fundamental hardness limits for independent learning in decentralized multi-agent environments, proving that polynomial-time solutions are unlikely under standard complexity assumptions. To address this barrier, the authors introduce a novel layered optimistic mirror descent algorithm that achieves sub-exponential convergence without requiring specific structural constraints on the game. These findings advance theoretical understanding of scalable algorithms for general-sum Markov games, offering a practical pathway toward robust multi-agent coordination in complex settings.
Independent Reinforcement Learning in Discounted Markov Games
arXiv:2609.00504v1 Announce Type: cross Abstract: In this work, we study radically uncoupled learning in discounted general-sum Markov games. Assuming ``$\mathsf{ETH}$ for $\mathsf{PPAD}$", we show that, for every fixed discount factor, there is no polynomial-time algorithm for computing inverse-polynomially accurate coarse correlated equilibria in discounted general-sum Markov games when players learn independently in decentralized settings. Complementing this hardness result, we provide what appears to be the first \emph{radically uncoupled} algorithm with sub-exponential convergence guarantees to coarse correlated equilibria in discounted general-sum Markov games without imposing any structural restrictions on the game. Our algorithm is a \emph{layered} variant of optimistic mirror descent with an increasing step-size schedule tailored to the multi-agent setting. Finally, we develop both full-feedback and partial feedback versions of the aforementioned algorithm and establish sub-exponential convergence guarantees for each case.
Abstract:In this work, we study radically uncoupled learning in discounted general-sum Markov games. Assuming ``$\mathsf{ETH}$ for $\mathsf{PPAD}$", we show that, for every fixed discount factor, there is no polynomial-time algorithm for computing inverse-polynomially accurate coarse correlated equilibria in discounted general-sum Markov games when players learn independently in decentralized settings. Complementing this hardness result, we provide what appears to be the first \emph{radically uncoupled} algorithm with sub-exponential convergence guarantees to coarse correlated equilibria in discounted general-sum Markov games without imposing any structural restrictions on the game. Our algorithm is a \emph{layered} variant of optimistic mirror descent with an increasing step-size schedule tailored to the multi-agent setting. Finally, we develop both full-feedback and partial feedback versions of the aforementioned algorithm and establish sub-exponential convergence guarantees for each case.
Computer Science and Game Theory (cs.GT); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Systems and Control (eess.SY); Optimization and Control (math.OC)
arXiv:2609.00504 [cs.GT]
(or arXiv:2609.00504v1 [cs.GT] for this version)
https://doi.org/10.48550/arXiv.2609.00504 arXiv-issued DOI via DataCite (pending registration)
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