mlsanityData to 7 Oct 2026

Mean Field Games Flock! The Reinforcement Learning Way

arXiv 2105.07933 ↗First posted 17 May 2021cs.MA cs.AIcited by 30

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Abstract (arXiv)

We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is tractable only in small dimensions. We phrase this problem as a Mean Field Game (MFG), where each individual chooses its acceleration depending on the population behavior. Combining Deep Reinforcement Learning (RL) and Normalizing Flows (NF), we obtain a tractable solution requiring only very weak assumptions. Our algorithm finds a Nash Equilibrium and the agents adapt their velocity to match the neighboring flock's average one. We use Fictitious Play and alternate: (1) computing an approximate best response with Deep RL, and (2) estimating the next population distribution with NF. We show numerically that our algorithm learn multi-group or high-dimensional flocking with obstacles.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 11 of its 34 references that are in the map. First posted on arXiv 17 May 2021.

Builds on

11 of 34 references.

References · 11

  1. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,635
  2. 2015Continuous control with deep reinforcement learningcited by 3,279
  3. 2015Trust Region Policy Optimizationcited by 2,503
  4. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2019Neural Spline Flowscited by 590
  6. 2019A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problemscited by 95
  7. 2020Fictitious Play for Mean Field Games: Continuous Time Analysis and Applicationscited by 57
  8. 2019On the Convergence of Model Free Learning in Mean Field Gamescited by 45
  9. 2015Learning in Mean Field Games: the Fictitious Playcited by 37
  10. 2018Optimal consensus control of the Cucker-Smale modelcited by 5
  11. 2019Deterministic mean field games with control on the accelerationcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 8; 2023: 3; 2024: 7; 2025: 5; 2026: 3.

30 papers.

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  1. 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 33
  2. 2021Generalization in Mean Field Games by Learning Master Policiescited by 28
  3. 2021Learning Graphon Mean Field Games and Approximate Nash Equilibriacited by 28
  4. 2022Policy Mirror Ascent for Efficient and Independent Learning in Mean Field Gamescited by 24
  5. 2022Oracle-free Reinforcement Learning in Mean-Field Games along a Single Sample Pathcited by 16
  6. 2021Reinforcement Learning for Mean Field Games, with Applications to Economicscited by 14
  7. 2022Learning Sparse Graphon Mean Field Gamescited by 14
  8. 2022Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependencecited by 13
  9. 2022A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learningcited by 12
  10. 2023Learning Decentralized Partially Observable Mean Field Control for Artificial Collective Behaviorcited by 6
  11. 2023Deep Reinforcement Learning for Infinite Horizon Mean Field Problems in Continuous Spacescited by 6
  12. 2024Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithmcited by 5
18 more
  1. 2024Stochastic Semi-Gradient Descent for Learning Mean Field Games with Population-Aware Function Approximationcited by 5
  2. 2021Exploration noise for learning linear-quadratic mean field gamescited by 3
  3. 2022Cooperation and Competition: Flocking with Evolutionary Multi-Agent Reinforcement Learningcited by 3
  4. 2024Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approachcited by 3
  5. 2022Developing, Evaluating and Scaling Learning Agents in Multi-Agent Environmentscited by 2
  6. 2024A Single Online Agent Can Efficiently Learn Mean Field Gamescited by 2
  7. 2025Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Gamescited by 2
  8. 2025Solving Continuous Mean Field Games: Deep Reinforcement Learning for Non-Stationary Dynamicscited by 2
  9. 2024Scalable Offline Reinforcement Learning for Mean Field Gamescited by 1
  10. 2026Bench-MFG: A Benchmark Suite for Learning in Stationary Mean Field Gamescited by 1
  11. 2023Networked Communication for Decentralised Agents in Mean-Field Gamescited by 0
  12. 2024Mean Field Correlated Imitation Learningcited by 0
  13. 2024Networked Communication for Mean-Field Games with Function Approximation and Empirical Mean-Field Estimationcited by 0
  14. 2025Causal Mean Field Multi-Agent Reinforcement Learningcited by 0
  15. 2025Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equationscited by 0
  16. 2025Bi-level Mean Field: Dynamic Grouping for Large-Scale MARLcited by 0
  17. 2026Recurrent Structural Policy Gradient for Partially Observable Mean Field Gamescited by 0
  18. 2026Towards Model-Free Learning in Dynamic Population Games: An Application to Karma Economiescited by 0