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Entropy Regularization for Mean Field Games with Learning

arXiv 2010.00145 ↗First posted 30 Sep 2020math.OC cs.LG stat.MLcited by 50

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Abstract (arXiv)

Entropy regularization has been extensively adopted to improve the efficiency, the stability, and the convergence of algorithms in reinforcement learning. This paper analyzes both quantitatively and qualitatively the impact of entropy regularization for Mean Field Game (MFG) with learning in a finite time horizon. Our study provides a theoretical justification that entropy regularization yields time-dependent policies and, furthermore, helps stabilizing and accelerating convergence to the game equilibrium. In addition, this study leads to a policy-gradient algorithm for exploration in MFG. Under this algorithm, agents are able to learn the optimal exploration scheduling, with stable and fast convergence to the game equilibrium.

Key facts. Cited by 50 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Sep 2020.

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Citing papers per year: 2021: 7; 2022: 7; 2023: 11; 2024: 12; 2025: 5; 2026: 8.

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  1. 2021Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithmscited by 76
  2. 2021Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space: A Martingale Approachcited by 62
  3. 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 33
  4. 2021Generalization in Mean Field Games by Learning Master Policiescited by 28
  5. 2023A mean-field games laboratory for generative modelingcited by 28
  6. 2022Policy Mirror Ascent for Efficient and Independent Learning in Mean Field Gamescited by 24
  7. 2021Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controlscited by 21
  8. 2023Actor-Critic learning for mean-field control in continuous timecited by 19
  9. 2021Exploration-exploitation trade-off for continuous-time episodic reinforcement learning with linear-convex modelscited by 18
  10. 2021Robust Risk-Aware Reinforcement Learningcited by 17
  11. 2023Continuous-time q-learning for mean-field control problemscited by 17
  12. 2022Learning Sparse Graphon Mean Field Gamescited by 14
38 more
  1. 2023On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximationcited by 13
  2. 2022A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learningcited by 12
  3. 2023Fast Policy Learning for Linear Quadratic Control with Entropy Regularizationcited by 11
  4. 2024Entropy annealing for policy mirror descent in continuous time and spacecited by 9
  5. 2025Accuracy of Discretely Sampled Stochastic Policies in Continuous-time Reinforcement Learningcited by 9
  6. 2021Adversarial Inverse Reinforcement Learning for Mean Field Gamescited by 8
  7. 2024Unified continuous-time q-learning for mean-field game and mean-field control problemscited by 7
  8. 2023A Policy Gradient Framework for Stochastic Optimal Control Problems with Global Convergence Guaranteecited by 6
  9. 2023Deep Reinforcement Learning for Infinite Horizon Mean Field Problems in Continuous Spacescited by 6
  10. 2023Data-Driven Merton's Strategies via Policy Randomizationcited by 6
  11. 2022Optimal scheduling of entropy regulariser for continuous-time linear-quadratic reinforcement learningcited by 5
  12. 2024Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penaltycited by 5
  13. 2026Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundationscited by 5
  14. 2023Finding Regularized Competitive Equilibria of Heterogeneous Agent Macroeconomic Models with Reinforcement Learningcited by 4
  15. 2024Convergence Analysis for Entropy-Regularized Control Problems: A Probabilistic Approachcited by 4
  16. 2022Hypergraphon Mean Field Gamescited by 3
  17. 2024Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approachcited by 3
  18. 2024Reinforcement Learning for Intensity Control: An Application to Choice-Based Network Revenue Managementcited by 3
  19. 2025Efficient Learning for Entropy-Regularized Markov Decision Processes via Multilevel Monte Carlocited by 3
  20. 2025Continuous Q-Score Matching: Diffusion Guided Reinforcement Learning for Continuous-Time Controlcited by 3
  21. 2026Model-free policy gradient for discrete-time mean-field controlcited by 3
  22. 2026Continuous-time q-learning for mean-field control with common noise, part-II: q-learning algorithmscited by 3
  23. 2026Deterministic Policy Gradient for Learning Equilibrium in Time-Inconsistent Control Problemscited by 3
  24. 2022Choquet regularization for reinforcement learningcited by 2
  25. 2023Learning Discrete-Time Major-Minor Mean Field Gamescited by 2
  26. 2024Policy Optimization finds Nash Equilibrium in Regularized General-Sum LQ Gamescited by 2
  27. 2024A Single Online Agent Can Efficiently Learn Mean Field Gamescited by 2
  28. 2024Reinforcement Learning for Jump-Diffusions, with Financial Applicationscited by 2
  29. 2024On the grid-sampling limit SDEcited by 2
  30. 2024A random measure approach to reinforcement learning in continuous timecited by 1
  31. 2023Networked Communication for Decentralised Agents in Mean-Field Gamescited by 0
  32. 2024Bounded Rationality Equilibrium Learning in Mean Field Gamescited by 0
  33. 2025A Robust Model-Based Approach for Continuous-Time Policy Evaluation with Unknown L'evy Process Dynamicscited by 0
  34. 2025Policy Transfer for Continuous-Time Reinforcement Learning: A (Rough) Differential Equation Approachcited by 0
  35. 2026Reinforcement Learning for Speculative Trading under Exploratory Frameworkcited by 0
  36. 2026Entropy Regularized Reinforcement Learning for Zero-Sum Stochastic Differential Games in a Regime-Switching Jump-Diffusion Processcited by 0
  37. 2026Entropy Regularization Improves Policy Robustness in Continuous-Time Reinforcement Learningcited by 0
  38. 2026Reinforcement Learning for Continuous-Time Jump Markov Decision Processes with Applications to Network Dynamic Pricingcited by 0