# Policy Iteration Reinforcement Learning Method for Continuous-Time Linear-Quadratic Mean-Field Control Problems

arXiv: https://arxiv.org/abs/2305.00424 · HTML: https://mlsanity.com/paper/2305.00424/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2023.

## Built on by (most cited first, 4 of 4)

- [Reconciling Discrete-Time Mixed Policies and Continuous-Time Relaxed Controls in Reinforcement Learning and Stochastic Control](https://mlsanity.com/paper/2504.21793/) (2025)
- [Robust Mean Field Social Control: A Unified Reinforcement Learning Framework](https://mlsanity.com/paper/2502.20029/) (2025)
- [Model-Free Q-Learning for Infinite-Horizon Stochastic Linear Quadratic Problems with Regime Switching](https://mlsanity.com/paper/2607.26456/) (2026)
- [Decentralized Strategies for Finite Population LQG Social Control: A Reinforcement Learning Approach](https://mlsanity.com/paper/2608.30244/) (2026)

## Abstract (arXiv)

This paper employs a policy iteration reinforcement learning (RL) method to study continuous-time linear-quadratic mean-field control problems in infinite horizon. The drift and diffusion terms in the dynamics involve the states, the controls, and their conditional expectations. We investigate the stabilizability and convergence of the RL algorithm using a Lyapunov Recursion. Instead of solving a pair of coupled Riccati equations, the RL technique focuses on strengthening an auxiliary function and the cost functional as the objective functions and updating the new policy to compute the optimal control via state trajectories. A numerical example sheds light on the established theoretical results.