mlsanityData to 7 Oct 2026

Exploration noise for learning linear-quadratic mean field games

arXiv 2107.00839 ↗First posted 2 Jul 2021math.OC cs.LG math.PRcited by 3

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Abstract (arXiv)

The goal of this paper is to demonstrate that common noise may serve as an exploration noise for learning the solution of a mean field game. This concept is here exemplified through a toy linear-quadratic model, for which a suitable form of common noise has already been proven to restore existence and uniqueness. We here go one step further and prove that the same form of common noise may force the convergence of the learning algorithm called `fictitious play', and this without any further potential or monotone structure. Several numerical examples are provided in order to support our theoretical analysis.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 21 of its 63 references that are in the map. First posted on arXiv 2 Jul 2021.

Builds on

21 of 63 references.

References · 21

  1. 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 188
  2. 2017Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equationscited by 62
  3. 2020Fictitious Play for Mean Field Games: Continuous Time Analysis and Applicationscited by 57
  4. 2019Model-Free Mean-Field Reinforcement Learning: Mean-Field MDP and Mean-Field Q-Learningcited by 56
  5. 2021Concave Utility Reinforcement Learning: the Mean-Field Game Viewpointcited by 54
  6. 2019On the Convergence of Model Free Learning in Mean Field Gamescited by 45
  7. 2015Learning in Mean Field Games: the Fictitious Playcited by 37
  8. 2019Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Casecited by 34
  9. 2021Mean Field Games Flock! The Reinforcement Learning Waycited by 30
  10. 2019Linear-Quadratic Mean-Field Reinforcement Learning: Convergence of Policy Gradient Methodscited by 24
  11. 2020Mean Field Games and Applications: Numerical Aspectscited by 22
  12. 2020Exploratory LQG Mean Field Games with Entropy Regularizationcited by 11
9 more
  1. 2017Learning in anonymous nonatomic games with applications to first-order mean field gamescited by 10
  2. 2016Proximal methods for stationary Mean Field Games with local couplingscited by 9
  3. 2018On the implementation of a primal-dual algorithm for second order time-dependent mean field games with local couplingscited by 9
  4. 2018Finite mean field games: fictitious play and convergence to a first order continuous mean field gamecited by 9
  5. 2019A Game-Theoretic Framework for Autonomous Vehicles Velocity Control: Bridging Microscopic Differential Games and Macroscopic Mean Field Gamescited by 9
  6. 2016Mean Field Type Control with Congestion (II): An Augmented Lagrangian Methodcited by 5
  7. 2018A model for system uncertainty in reinforcement learningcited by 1
  8. 2019Finite state Mean Field Games with Wright-Fisher common noisecited by 1
  9. 2020Selection by vanishing common noise for potential finite state mean field gamescited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 0; 2025: 0; 2026: 1.

3 papers.

  1. 2023Recent Developments in Machine Learning Methods for Stochastic Control and Gamescited by 19
  2. 2022Learning Sparse Graphon Mean Field Gamescited by 14
  3. 2026Stationary Robust Mean-Field Games under Model Mismatchescited by 0