# Decentralized Strategies for Finite Population LQG Social Control: A Reinforcement Learning Approach

arXiv: https://arxiv.org/abs/2608.30244 · HTML: https://mlsanity.com/paper/2608.30244/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 20 of its 51 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 20 of 20)

- [Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications](https://mlsanity.com/paper/2007.03458/) (2020)
- [Entropy Regularization for Mean Field Games with Learning](https://mlsanity.com/paper/2010.00145/) (2020)
- [Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysis](https://mlsanity.com/paper/2002.04131/) (2020)
- [Unified Reinforcement Q-Learning for Mean Field Game and Control Problems](https://mlsanity.com/paper/2006.13912/) (2020)
- [Breaking the Curse of Many Agents: Provable Mean Embedding Q-Iteration for Mean-Field Reinforcement Learning](https://mlsanity.com/paper/2006.11917/) (2020)
- [Robust Policy Iteration for Continuous-time Linear Quadratic Regulation](https://mlsanity.com/paper/2005.09528/) (2020)
- [Graphon Mean Field Games and the GMFG Equations](https://mlsanity.com/paper/2008.10216/) (2020)
- [Proximal methods for stationary Mean Field Games with local couplings](https://mlsanity.com/paper/1608.07701/) (2016)
- [Graphon Mean-Field Control for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.04808/) (2022)
- [Robust Reinforcement Learning for Risk-Sensitive Linear Quadratic Gaussian Control](https://mlsanity.com/paper/2212.02072/) (2022)
- [Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics](https://mlsanity.com/paper/1701.09118/) (2017)
- [Linear-Quadratic N-person and Mean-Field Games with Ergodic Cost](https://mlsanity.com/paper/1401.1421/) (2014)
- [Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown L2-Disturbance](https://mlsanity.com/paper/1701.00196/) (2017)
- [On the convergence of closed-loop Nash equilibria to the mean field game limit](https://mlsanity.com/paper/1808.02745/) (2018)
- [Linear quadratic mean field social optimization: Asymptotic solvability and decentralized control](https://mlsanity.com/paper/2012.15468/) (2020)
- [Policy Iteration Reinforcement Learning Method for Continuous-Time Linear-Quadratic Mean-Field Control Problems](https://mlsanity.com/paper/2305.00424/) (2023)
- [Mean Field LQG Social Optimization: A Reinforcement Learning Approach](https://mlsanity.com/paper/2410.15119/) (2024)
- [Mean Field Linear Quadratic Control: Uniform Stabilization and Social Optimality](https://mlsanity.com/paper/2002.12363/) (2020)
- [Decentralized Strategies for Finite Population Linear-Quadratic-Gaussian Games and Teams](https://mlsanity.com/paper/2206.05754/) (2022)
- [Linear-Quadratic Mean-Field Game for Stochastic Systems with Partial Observation](https://mlsanity.com/paper/2408.09652/) (2024)

## Abstract (arXiv)

This paper presents a novel model-free algorithm for the finite-population linear quadratic Gaussian (LQG) decentralized social control problem with multiplicative noise. The state and control weights in the cost functional are not limited to be positive semidefinite. For both finite-horizon and infinite-horizon cases, the goal is to obtain a social optimum by solving two algebraic Riccati equations (AREs), without requiring prior knowledge of the system matrices. Then, we complete the design of a model-free algorithm for solving the decentralized social control problem. Especially, in the infinite-horizon case, the algorithm's convergence is based on analyzing the spectral property of the Lyapunov-type operator. The differences of reinforcement learning (RL) solutions between the finite-horizon and infinite-horizon cases are compared. Finally, the effectiveness of the proposed algorithm is demonstrated by a numerical example.