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This monograph is a theory-heavy introduction to reinforcement learning for large populations of interacting agents, covering dynamic programming, propagation-of-chaos limits, and convergence analyses of tabular Q-learning and policy-gradient methods. Its practical value is the formal bridge it builds between multi-agent RL and mean field control, plus guidance on when a large-population learning problem is tractable. Readers should note that the deep RL material, such as deep deterministic policy gradient, is presented as numerical illustration rather than as a source of new empirical results.
Mean Field Reinforcement Learning: Theory and Algorithms for Mean Field Control
arXiv:2607.01525v2 Announce Type: replace-cross Abstract: This monograph provides an introduction to mean field reinforcement learning through the lens of Markov decision processes arising from large-population stochastic control with mean field interactions and common noise. Starting from the connection between multi-agent reinforcement learning and mean field control, it develops the probabilistic, mathematical, and control-theoretic framework needed to formulate representative-agent learning problems, analyze their relationship with finite-population systems, and study both general and linear-quadratic models. The presentation includes dynamic programming principles, propagation-of-chaos limits, and theoretical analyses of tabular Q-learning and policy-gradient methods. It also discusses numerical implementations, including tabular schemes and deep reinforcement learning methods such as deep deterministic policy gradient. The goal is to give readers a coherent bridge between mean field control theory and reinforcement learning methodology, emphasizing the mathematical structure of the problems and the design of tractable learning approaches for large stochastic populations.
Abstract:This monograph provides an introduction to mean field reinforcement learning through the lens of Markov decision processes arising from large-population stochastic control with mean field interactions and common noise. Starting from the connection between multi-agent reinforcement learning and mean field control, it develops the probabilistic, mathematical, and control-theoretic framework needed to formulate representative-agent learning problems, analyze their relationship with finite-population systems, and study both general and linear-quadratic models. The presentation includes dynamic programming principles, propagation-of-chaos limits, and theoretical analyses of tabular Q-learning and policy-gradient methods. It also discusses numerical implementations, including tabular schemes and deep reinforcement learning methods such as deep deterministic policy gradient. The goal is to give readers a coherent bridge between mean field control theory and reinforcement learning methodology, emphasizing the mathematical structure of the problems and the design of tractable learning approaches for large stochastic populations.
Optimization and Control (math.OC); Machine Learning (cs.LG); Multiagent Systems (cs.MA); Probability (math.PR)
arXiv:2607.01525 [math.OC]
(or arXiv:2607.01525v2 [math.OC] for this version)
https://doi.org/10.48550/arXiv.2607.01525 Focus to learn more arXiv-issued DOI via DataCite
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