mlsanityData to 14 Oct 2026

Q-Learning in Regularized Mean-field Games

arXiv 2003.12151 ↗First posted 24 Mar 2020math.OC cs.LG cs.SYcited by 42

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Abstract (arXiv)

In this paper, we introduce a regularized mean-field game and study learning of this game under an infinite-horizon discounted reward function. Regularization is introduced by adding a strongly concave regularization function to the one-stage reward function in the classical mean-field game model. We establish a value iteration based learning algorithm to this regularized mean-field game using fitted Q-learning. The regularization term in general makes reinforcement learning algorithm more robust to the system components. Moreover, it enables us to establish error analysis of the learning algorithm without imposing restrictive convexity assumptions on the system components, which are needed in the absence of a regularization term.

Key facts. Cited by 42 papers in the map (data through 14 Oct 2026). First posted on arXiv 24 Mar 2020.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 6; 2022: 8; 2023: 6; 2024: 13; 2025: 6; 2026: 3.

42 papers.

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  1. 2021Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learningcited by 73
  2. 2021Concave Utility Reinforcement Learning: the Mean-Field Game Viewpointcited by 56
  3. 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 38
  4. 2021Scaling up Mean Field Games with Online Mirror Descentcited by 32
  5. 2021Generalization in Mean Field Games by Learning Master Policiescited by 28
  6. 2022Policy Mirror Ascent for Efficient and Independent Learning in Mean Field Gamescited by 26
  7. 2023Recent Developments in Machine Learning Methods for Stochastic Control and Gamescited by 24
  8. 2022Oracle-free Reinforcement Learning in Mean-Field Games along a Single Sample Pathcited by 20
  9. 2021Reinforcement Learning for Mean Field Games, with Applications to Economicscited by 15
  10. 2022A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learningcited by 14
  11. 2022Learning Sparse Graphon Mean Field Gamescited by 14
  12. 2023On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximationcited by 14
30 more
  1. 2024Unified continuous-time q-learning for mean-field game and mean-field control problemscited by 13
  2. 2023On Imitation in Mean-field Gamescited by 10
  3. 2023Learning Regularized Monotone Graphon Mean-Field Gamescited by 9
  4. 2024Model-Based RL for Mean-Field Games is not Statistically Harder than Single-Agent RLcited by 9
  5. 2021Adversarial Inverse Reinforcement Learning for Mean Field Gamescited by 8
  6. 2024When is Mean-Field Reinforcement Learning Tractable and Relevant?cited by 8
  7. 2022Learning Correlated Equilibria in Mean-Field Gamescited by 6
  8. 2024Population-aware Online Mirror Descent for Mean-Field Games by Deep Reinforcement Learningcited by 5
  9. 2024Stochastic Semi-Gradient Descent for Learning Mean Field Games with Population-Aware Function Approximationcited by 5
  10. 2024Maximum Causal Entropy IRL in Mean-Field Games and GNEP Framework for Forward RLcited by 4
  11. 2025Population-aware Online Mirror Descent for Mean-Field Games with Common Noise by Deep Reinforcement Learningcited by 4
  12. 2026Model-free policy gradient for discrete-time mean-field controlcited by 4
  13. 2024Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approachcited by 3
  14. 2024Learning in Herding Mean Field Games: Single-Loop Algorithm with Finite-Time Convergence Analysiscited by 3
  15. 2025Efficient Learning for Entropy-Regularized Markov Decision Processes via Multilevel Monte Carlocited by 3
  16. 2025Convergence of Actor-Critic Learning for Mean Field Games and Mean Field Control in Continuous Spacescited by 3
  17. 2022Review of Metrics to Measure the Stability, Robustness and Resilience of Reinforcement Learningcited by 2
  18. 2024A Single Online Agent Can Efficiently Learn Mean Field Gamescited by 2
  19. 2024Exploiting Approximate Symmetry for Efficient Multi-Agent Reinforcement Learningcited by 2
  20. 2025Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Gamescited by 2
  21. 2022Scalable Task-Driven Robotic Swarm Control via Collision Avoidance and Learning Mean-Field Controlcited by 1
  22. 2023Reinforcement Learning for SBM Graphon Games with Re-Samplingcited by 1
  23. 2025On the Statistical Complexity for Offline and Low-Adaptive Reinforcement Learning with Structurescited by 1
  24. 2023Networked Communication for Decentralised Agents in Mean-Field Gamescited by 0
  25. 2024Networked Communication for Mean-Field Games with Function Approximation and Empirical Mean-Field Estimationcited by 0
  26. 2024Last Iterate Convergence in Monotone Mean Field Gamescited by 0
  27. 2024Bounded Rationality Equilibrium Learning in Mean Field Gamescited by 0
  28. 2025Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equationscited by 0
  29. 2026Robust Q-learning for mean-field control under Wasserstein uncertainty in common noisecited by 0
  30. 2026Stationary Robust Mean-Field Games under Model Mismatchescited by 0