Convergence of Decentralized Actor-Critic Algorithm in General-sum Markov Games
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Abstract (arXiv)
Markov games provide a powerful framework for modeling strategic multi-agent interactions in dynamic environments. Traditionally, convergence properties of decentralized learning algorithms in these settings have been established only for special cases, such as Markov zero-sum and potential games, which do not fully capture real-world interactions. In this paper, we address this gap by studying the asymptotic properties of learning algorithms in general-sum Markov games. In particular, we focus on a decentralized algorithm where each agent adopts an actor-critic learning dynamic with asynchronous step sizes. This decentralized approach enables agents to operate independently, without requiring knowledge of others' strategies or payoffs. We introduce the concept of a Markov Near-Potential Function (MNPF) and demonstrate that it serves as an approximate Lyapunov function for the policy updates in the decentralized learning dynamics, which allows us to characterize the convergent set of strategies. We further strengthen our result under specific regularity conditions and with finite Nash equilibria.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 12 of its 26 references that are in the map. First posted on arXiv 6 Sep 2024.
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12 of 26 references.
References · 12
- 2016Safe, Multi-Agent, Reinforcement Learning for Autonomous Drivingcited by 301
- 2021V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RLcited by 111
- 2021Independent Policy Gradient Methods for Competitive Reinforcement Learningcited by 97
- 2021Last-iterate Convergence of Decentralized Optimistic Gradient Descent/Ascent in Infinite-horizon Competitive Markov Gamescited by 66
- 2022Independent Policy Gradient for Large-Scale Markov Potential Games: Sharper Rates, Function Approximation, and Game-Agnostic Convergencecited by 54
- 2021Decentralized Q-Learning in Zero-sum Markov Gamescited by 53
- 2021Provably Efficient Reinforcement Learning in Decentralized General-Sum Markov Gamescited by 42
- 2015Decentralized Q-Learning for Stochastic Teams and Gamescited by 34
- 2021Independent Natural Policy Gradient Always Converges in Markov Potential Gamescited by 34
- 2022Independent and Decentralized Learning in Markov Potential Gamescited by 19
- 2019Decentralized Learning for Optimality in Stochastic Dynamic Teams and Games with Local Control and Global State Informationcited by 12
- 2023Unsynchronized Decentralized Q-Learning: Two Timescale Analysis By Persistencecited by 3
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Citing papers per year: 2026: 2.
2 papers.