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Mean Field Multi-Agent Reinforcement Learning

arXiv 1802.05438 ↗First posted 15 Feb 2018cs.MA cs.AI cs.LGcited by 202

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Abstract (arXiv)

Existing multi-agent reinforcement learning methods are limited typically to a small number of agents. When the agent number increases largely, the learning becomes intractable due to the curse of the dimensionality and the exponential growth of agent interactions. In this paper, we present Mean Field Reinforcement Learning where the interactions within the population of agents are approximated by those between a single agent and the average effect from the overall population or neighboring agents; the interplay between the two entities is mutually reinforced: the learning of the individual agent's optimal policy depends on the dynamics of the population, while the dynamics of the population change according to the collective patterns of the individual policies. We develop practical mean field Q-learning and mean field Actor-Critic algorithms and analyze the convergence of the solution to Nash equilibrium. Experiments on Gaussian squeeze, Ising model, and battle games justify the learning effectiveness of our mean field approaches. In addition, we report the first result to solve the Ising model via model-free reinforcement learning methods.

Key facts. Cited by 202 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Feb 2018.

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Citing papers per year: 2020: 1; 2021: 37; 2022: 34; 2023: 31; 2024: 34; 2025: 36; 2026: 29.

202 papers.

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  1. 2021MetaDrive: Composing Diverse Driving Scenarios for Generalizable Reinforcement Learningcited by 281
  2. 2022SMACv2: An Improved Benchmark for Cooperative Multi-Agent Reinforcement Learningcited by 118
  3. 2021Scaling Multi-Agent Reinforcement Learning with Selective Parameter Sharingcited by 85
  4. 2023Heterogeneous-Agent Reinforcement Learningcited by 67
  5. 2021Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learningcited by 65
  6. 2021Cooperative Exploration for Multi-Agent Deep Reinforcement Learningcited by 57
  7. 2021Concave Utility Reinforcement Learning: the Mean-Field Game Viewpointcited by 54
  8. 2024Learning Multi-Agent Communication from Graph Modeling Perspectivecited by 47
  9. 2021Settling the Variance of Multi-Agent Policy Gradientscited by 45
  10. 2021Deep Multiagent Reinforcement Learning: Challenges and Directionscited by 42
  11. 2021Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learningcited by 38
  12. 2021Shapley Counterfactual Credits for Multi-Agent Reinforcement Learningcited by 37
38 more
  1. 2021Reinforcement Learning for Ridesharing: An Extended Surveycited by 35
  2. 2023Robust Multi-Agent Reinforcement Learning with State Uncertaintycited by 35
  3. 2021Applications of Multi-Agent Reinforcement Learning in Future Internet: A Comprehensive Surveycited by 34
  4. 2021Learning to Simulate Self-Driven Particles System with Coordinated Policy Optimizationcited by 33
  5. 2023Robust Multi-Agent Reinforcement Learning via Adversarial Regularization: Theoretical Foundation and Stable Algorithmscited by 25
  6. 2021Model-based Multi-agent Policy Optimization with Adaptive Opponent-wise Rolloutscited by 24
  7. 2021A Cooperative-Competitive Multi-Agent Framework for Auto-bidding in Online Advertisingcited by 22
  8. 2022Solving Continuous Control via Q-learningcited by 21
  9. 2022A Survey on Reinforcement Learning in Aviation Applicationscited by 19
  10. 2023Maximum Entropy Heterogeneous-Agent Reinforcement Learningcited by 19
  11. 2021Online Double Oraclecited by 18
  12. 2021Semantic Tracklets: An Object-Centric Representation for Visual Multi-Agent Reinforcement Learningcited by 18
  13. 2021On the Complexity of Computing Markov Perfect Equilibrium in General-Sum Stochastic Gamescited by 18
  14. 2022Influencing Long-Term Behavior in Multiagent Reinforcement Learningcited by 18
  15. 2022Global Convergence of Localized Policy Iteration in Networked Multi-Agent Reinforcement Learningcited by 18
  16. 2021ROMAX: Certifiably Robust Deep Multiagent Reinforcement Learning via Convex Relaxationcited by 17
  17. 2021Survey of Recent Multi-Agent Reinforcement Learning Algorithms Utilizing Centralized Trainingcited by 16
  18. 2022An Introduction to Multi-Agent Reinforcement Learning and Review of its Application to Autonomous Mobilitycited by 16
  19. 2022RoMFAC: A robust mean-field actor-critic reinforcement learning against adversarial perturbations on statescited by 16
  20. 2025SEDM: Scalable Self-Evolving Distributed Memory for Agentscited by 16
  21. 2021Learning to Optimize Industry-Scale Dynamic Pickup and Delivery Problemscited by 15
  22. 2021Reinforcement Learning for Mean Field Games, with Applications to Economicscited by 14
  23. 2022Efficient Model-based Multi-agent Reinforcement Learning via Optimistic Equilibrium Computationcited by 14
  24. 2025Multi-Agent Reinforcement Learning for Resources Allocation Optimization: A Surveycited by 14
  25. 2021Permutation Invariant Policy Optimization for Mean-Field Multi-Agent Reinforcement Learning: A Principled Approachcited by 13
  26. 2023Parameter Sharing with Network Pruning for Scalable Multi-Agent Deep Reinforcement Learningcited by 13
  27. 2023On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximationcited by 13
  28. 2022Autonomy and Intelligence in the Computing Continuum: Challenges, Enablers, and Future Directions for Orchestrationcited by 12
  29. 2022A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learningcited by 12
  30. 2024Hierarchical Consensus-Based Multi-Agent Reinforcement Learning for Multi-Robot Cooperation Taskscited by 12
  31. 2025MF-LLM: Simulating Population Decision Dynamics via a Mean-Field Large Language Model Frameworkcited by 12
  32. 2022Policy Diagnosis via Measuring Role Diversity in Cooperative Multi-agent RLcited by 11
  33. 2023A Versatile Multi-Agent Reinforcement Learning Benchmark for Inventory Managementcited by 9
  34. 2023Canaries and Whistles: Resilient Drone Communication Networks with (or without) Deep Reinforcement Learningcited by 9
  35. 2024Mean-Field Sampling for Cooperative Multi-Agent Reinforcement Learningcited by 9
  36. 2021Adversarial Inverse Reinforcement Learning for Mean Field Gamescited by 8
  37. 2022Efficient Policy Space Response Oraclescited by 8
  38. 2022Interaction Pattern Disentangling for Multi-Agent Reinforcement Learningcited by 8

50 most cited of 202 All 202 (JSON)