# Exploration noise for learning linear-quadratic mean field games

arXiv: https://arxiv.org/abs/2107.00839 · HTML: https://mlsanity.com/paper/2107.00839/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 63 references that are in the map.
- First posted on arXiv 2 Jul 2021.

## Builds on (most cited first, 21 of 21)

- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations](https://mlsanity.com/paper/1709.05963/) (2017)
- [Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications](https://mlsanity.com/paper/2007.03458/) (2020)
- [Model-Free Mean-Field Reinforcement Learning: Mean-Field MDP and Mean-Field Q-Learning](https://mlsanity.com/paper/1910.12802/) (2019)
- [Concave Utility Reinforcement Learning: the Mean-Field Game Viewpoint](https://mlsanity.com/paper/2106.03787/) (2021)
- [On the Convergence of Model Free Learning in Mean Field Games](https://mlsanity.com/paper/1907.02633/) (2019)
- [Learning in Mean Field Games: the Fictitious Play](https://mlsanity.com/paper/1507.06280/) (2015)
- [Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Case](https://mlsanity.com/paper/1908.01613/) (2019)
- [Mean Field Games Flock! The Reinforcement Learning Way](https://mlsanity.com/paper/2105.07933/) (2021)
- [Linear-Quadratic Mean-Field Reinforcement Learning: Convergence of Policy Gradient Methods](https://mlsanity.com/paper/1910.04295/) (2019)
- [Mean Field Games and Applications: Numerical Aspects](https://mlsanity.com/paper/2003.04444/) (2020)
- [Exploratory LQG Mean Field Games with Entropy Regularization](https://mlsanity.com/paper/2011.12946/) (2020)
- [Proximal methods for stationary Mean Field Games with local couplings](https://mlsanity.com/paper/1608.07701/) (2016)
- [Learning in anonymous nonatomic games with applications to first-order mean field games](https://mlsanity.com/paper/1704.00378/) (2017)
- [On the implementation of a primal-dual algorithm for second order time-dependent mean field games with local couplings](https://mlsanity.com/paper/1802.07902/) (2018)
- [Finite mean field games: fictitious play and convergence to a first order continuous mean field game](https://mlsanity.com/paper/1805.05940/) (2018)
- [A Game-Theoretic Framework for Autonomous Vehicles Velocity Control: Bridging Microscopic Differential Games and Macroscopic Mean Field Games](https://mlsanity.com/paper/1903.06053/) (2019)
- [Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method](https://mlsanity.com/paper/1611.02023/) (2016)
- [A model for system uncertainty in reinforcement learning](https://mlsanity.com/paper/1802.07668/) (2018)
- [Finite state Mean Field Games with Wright-Fisher common noise](https://mlsanity.com/paper/1912.06701/) (2019)
- [Selection by vanishing common noise for potential finite state mean field games](https://mlsanity.com/paper/2005.12153/) (2020)

## Built on by (most cited first, 3 of 3)

- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Learning Sparse Graphon Mean Field Games](https://mlsanity.com/paper/2209.03880/) (2022)
- [Stationary Robust Mean-Field Games under Model Mismatches](https://mlsanity.com/paper/2606.22579/) (2026)

## 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.