mlsanityData to 14 Oct 2026

Robust Mean Field Social Control: A Unified Reinforcement Learning Framework

arXiv 2502.20029 ↗First posted 27 Feb 2025eess.SY cs.SYcited by 2

On the map: Deep reinforcement learning methods → RL for games and combinatorial optimization

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.

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.

Builds on

15 of 49 references.

Closest ancestors · 1

Same direction, newest first

  1. 2024Mean Field LQG Social Optimization: A Reinforcement Learning Approach19 Oct

Other references · 14

  1. 2021On the Approximation of Cooperative Heterogeneous Multi-Agent Reinforcement Learning (MARL) using Mean Field Control (MFC)cited by 32
  2. 2019Dynamic Programming Principles for Mean-Field Controls with Learningcited by 23
  3. 2020Robust Policy Iteration for Continuous-time Linear Quadratic Regulationcited by 15
  4. 2020Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Methodcited by 11
  5. 2020Optimal incentives to mitigate epidemics: a Stackelberg mean field game approachcited by 9
  6. 2022Robust Reinforcement Learning for Risk-Sensitive Linear Quadratic Gaussian Controlcited by 7
  7. 2023On stabilizability and exact observability of stochastic systems with their applicationscited by 5
  8. 2017Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown L2-Disturbancecited by 4
  9. 2019Social Optima in Robust Mean Field LQG Control: From Finite to Infinite Horizoncited by 4
  10. 2020Linear quadratic mean field social optimization: Asymptotic solvability and decentralized controlcited by 4
  11. 2023Policy Iteration Reinforcement Learning Method for Continuous-Time Linear-Quadratic Mean-Field Control Problemscited by 4
  12. 2024Robust Cooperative Multi-Agent Reinforcement Learning:A Mean-Field Type Game Perspectivecited by 4
2 more
  1. 2018An integral control formulation of Mean-field game based large scale coordination of loads in smart gridscited by 3
  2. 2020Indefinite Linear Quadratic Mean Field Social Control Problems with Multiplicative Noisecited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Stationary Robust Mean-Field Games under Model Mismatchescited by 0
  2. 2026Mean Field Reinforcement Learningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Reinforcement Learning for Discrete-time LQG Mean Field Social Control Problems with Unknown Dynamics
  2. 2026Inverse reinforcement learning for indefinite mean-field social optimization with multiplicative noise
  3. 2026Decentralized Strategies for Finite Population LQG Social Control: A Reinforcement Learning Approach
  4. 2026Data-Driven Network LQG Mean Field Games with Heterogeneous Populations via Integral Reinforcement Learning
  5. 2025Data-Driven Mean Field Equilibrium Computation in Large-Population LQG Games
  6. 2024Full error analysis of policy gradient learning algorithms for exploratory linear quadratic mean-field control problem in continuous time with common noise
  7. 2024Robust policy iteration for continuous-time stochastic H_∞ control problem with unknown dynamics
  8. 2025Policy Optimization for Continuous-time Linear-Quadratic Graphon Mean Field Games