# Exploratory LQG Mean Field Games with Entropy Regularization

arXiv: https://arxiv.org/abs/2011.12946 · HTML: https://mlsanity.com/paper/2011.12946/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

## Built on by (most cited first, 15 of 15)

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- [Policy Optimization finds Nash Equilibrium in Regularized General-Sum LQ Games](https://mlsanity.com/paper/2404.00045/) (2024)
- [A random measure approach to reinforcement learning in continuous time](https://mlsanity.com/paper/2409.17200/) (2024)
- [Entropy Regularized Reinforcement Learning for Zero-Sum Stochastic Differential Games in a Regime-Switching Jump-Diffusion Process](https://mlsanity.com/paper/2606.28669/) (2026)
- [Robust policy iteration for continuous-time stochastic H_∞ control problem with unknown dynamics](https://mlsanity.com/paper/2402.04721/) (2024)
- [Two Kinds of Learning Algorithms for Continuous-Time VWAP Targeting Execution](https://mlsanity.com/paper/2411.06645/) (2024)
- [Robust Q-learning for mean-field control under Wasserstein uncertainty in common noise](https://mlsanity.com/paper/2606.20356/) (2026)
- [Continuous-Time Reinforcement Learning for N-Player Stochastic Differential Games with Exploratory Policies](https://mlsanity.com/paper/2607.19928/) (2026)
- [Entropy-Regularized Mean-Field Games with Average-Reward Criterion: Span-Seminorm Contractions and Model-Free Learning](https://mlsanity.com/paper/2610.15871/) (2026)

## Abstract (arXiv)

We study a general class of entropy-regularized multi-variate LQG mean field games (MFGs) in continuous time with K distinct sub-population of agents. We extend the notion of actions to action distributions (exploratory actions), and explicitly derive the optimal action distributions for individual agents in the limiting MFG. We demonstrate that the optimal set of action distributions yields an ε-Nash equilibrium for the finite-population entropy-regularized MFG. Furthermore, we compare the resulting solutions with those of classical LQG MFGs and establish the equivalence of their existence.