# Robust Mean Field Social Control: A Unified Reinforcement Learning Framework

arXiv: https://arxiv.org/abs/2502.20029 · HTML: https://mlsanity.com/paper/2502.20029/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 15 of its 49 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## 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, 15 of 15)

- [On the Approximation of Cooperative Heterogeneous Multi-Agent Reinforcement Learning (MARL) using Mean Field Control (MFC)](https://mlsanity.com/paper/2109.04024/) (2021)
- [Dynamic Programming Principles for Mean-Field Controls with Learning](https://mlsanity.com/paper/1911.07314/) (2019)
- [Robust Policy Iteration for Continuous-time Linear Quadratic Regulation](https://mlsanity.com/paper/2005.09528/) (2020)
- [Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Method](https://mlsanity.com/paper/2011.14516/) (2020)
- [Optimal incentives to mitigate epidemics: a Stackelberg mean field game approach](https://mlsanity.com/paper/2011.03105/) (2020)
- [Robust Reinforcement Learning for Risk-Sensitive Linear Quadratic Gaussian Control](https://mlsanity.com/paper/2212.02072/) (2022)
- [On stabilizability and exact observability of stochastic systems with their applications](https://mlsanity.com/paper/2307.08915/) (2023)
- [Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown L2-Disturbance](https://mlsanity.com/paper/1701.00196/) (2017)
- [Social Optima in Robust Mean Field LQG Control: From Finite to Infinite Horizon](https://mlsanity.com/paper/1908.01122/) (2019)
- [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)
- [Robust Cooperative Multi-Agent Reinforcement Learning:A Mean-Field Type Game Perspective](https://mlsanity.com/paper/2406.13992/) (2024)
- [Mean Field LQG Social Optimization: A Reinforcement Learning Approach](https://mlsanity.com/paper/2410.15119/) (2024)
- [An integral control formulation of Mean-field game based large scale coordination of loads in smart grids](https://mlsanity.com/paper/1803.00040/) (2018)
- [Indefinite Linear Quadratic Mean Field Social Control Problems with Multiplicative Noise](https://mlsanity.com/paper/2009.09864/) (2020)

## Built on by (most cited first, 2 of 2)

- [Stationary Robust Mean-Field Games under Model Mismatches](https://mlsanity.com/paper/2606.22579/) (2026)
- [Mean Field Reinforcement Learning](https://mlsanity.com/paper/2607.01525/) (2026)

## Abstract (arXiv)

This paper studies linear quadratic Gaussian robust mean field social control problems in the presence of multiplicative noise. We aim to compute asymptotic decentralized strategies without requiring full prior knowledge of agents' dynamics. The primary challenges lie in solving an indefinite stochastic algebraic Riccati equation for feedback gains, and an indefinite algebraic Riccati equation for feedforward gains. To overcome these challenges, we first propose a unified dual-loop iterative framework that handles both indefinite Riccati-type equations, and provide rigorous convergence proofs for both the outer-loop and inner-loop iterations. Secondly, considering the potential biases arising in the iterative processes due to estimation and modeling errors, we verify the robustness of the proposed algorithm using the small-disturbance input-to-state stability technique. Convergence to a neighborhood of the optimal solution is thus ensured, even in the existence of disturbances. Finally, to relax the limitation of requiring precise knowledge of agents' dynamics, we employ the integral reinforcement learning technique to develop a data-driven method within the dual-loop iterative framework. A numerical example is provided to demonstrate the effectiveness of the proposed algorithm.