mlsanityData to 14 Oct 2026

Mean Field LQG Social Optimization: A Reinforcement Learning Approach

arXiv 2410.15119 ↗First posted 19 Oct 2024math.OCcited by 4

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

Abstract (arXiv)

This paper presents a novel model-free method to solve linear quadratic Gaussian mean field social control problems in the presence of multiplicative noise. The objective is to achieve a social optimum by solving two algebraic Riccati equations (AREs) and determining a mean field (MF) state, both without requiring prior knowledge of individual system dynamics for all agents. In the proposed approach, we first employ integral reinforcement learning techniques to develop two model-free iterative equations that converge to solutions for the stochastic ARE and the induced indefinite ARE respectively. Then, the MF state is approximated, either through the Monte Carlo method with the obtained gain matrices or through the system identification with the measured data. Notably, a unified state and input samples collected from a single agent are used in both iterations and identification procedure, making the method more computationally efficient and scalable. Finally, a numerical example is given to demonstrate the effectiveness of the proposed algorithm.

Key facts. Cited by 4 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 26 of its 63 references that are in the map. First posted on arXiv 19 Oct 2024.

Builds on

26 of 63 references.

References · 26

  1. 2019A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problemscited by 97
  2. 2021Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learningcited by 73
  3. 2020Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysiscited by 49
  4. 2020Unified Reinforcement Q-Learning for Mean Field Game and Control Problemscited by 49
  5. 2019On the Convergence of Model Free Learning in Mean Field Gamescited by 48
  6. 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 38
  7. 2021Mean Field Games Flock! The Reinforcement Learning Waycited by 31
  8. 2019Linear-Quadratic Mean-Field Reinforcement Learning: Convergence of Policy Gradient Methodscited by 28
  9. 2019Deep Learning Methods for Mean Field Control Problems with Delaycited by 25
  10. 2016Proximal methods for stationary Mean Field Games with local couplingscited by 11
  11. 2020Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Methodcited by 11
  12. 2020Reinforcement Learning in Non-Stationary Discrete-Time Linear-Quadratic Mean-Field Gamescited by 10
14 more
  1. 2019Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: I -- The Ergodic Casecited by 6
  2. 2021Policy iteration method for time-dependent Mean Field Games systems with non-separable Hamiltonianscited by 5
  3. 2023On stabilizability and exact observability of stochastic systems with their applicationscited by 5
  4. 2019Social Optima in Robust Mean Field LQG Control: From Finite to Infinite Horizoncited by 4
  5. 2020Linear quadratic mean field social optimization: Asymptotic solvability and decentralized controlcited by 4
  6. 2020Robust Mean Field Social Control Problems with Applications in Analysis of Opinion Dynamicscited by 3
  7. 2020Mean Field Linear Quadratic Control: Uniform Stabilization and Social Optimalitycited by 3
  8. 2020Indefinite Linear Quadratic Mean Field Social Control Problems with Multiplicative Noisecited by 3
  9. 2016Dynamic Collective Choice: Social Optimacited by 2
  10. 2018Mean Field Production Output Control with Sticky Prices: Nash and Social Solutionscited by 2
  11. 2020Team-Optimal Solution of Finite Number of Mean-Field Coupled LQG Subsystemscited by 2
  12. 2021Rates of convergence for the policy iteration method for Mean Field Games systemscited by 2
  13. 2019Mean Field Games for Multi-agent Systems with Multiplicative Noisescited by 1
  14. 2023An Addendum to the Problem of Zero-Sum LQ Stochastic Mean-Field Dynamic Games (Extended version)cited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 2.

4 papers.

  1. 2025Robust Mean Field Social Control: A Unified Reinforcement Learning Frameworkcited by 2
  2. 2025Reinforcement Learning for Discrete-time LQG Mean Field Social Control Problems with Unknown Dynamicscited by 0
  3. 2026Data-Driven Network LQG Mean Field Games with Heterogeneous Populations via Integral Reinforcement Learningcited by 0
  4. 2026Decentralized Strategies for Finite Population LQG Social Control: A Reinforcement Learning Approachcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Inverse reinforcement learning for indefinite mean-field social optimization with multiplicative noise
  2. 2025Data-Driven Mean Field Equilibrium Computation in Large-Population LQG Games
  3. 2026Mean Field Reinforcement Learning
  4. 2024Full error analysis of policy gradient learning algorithms for exploratory linear quadratic mean-field control problem in continuous time with common noise
  5. 2024Efficient and Scalable Deep Reinforcement Learning for Mean Field Control Games
  6. 2025Policy Optimization for Continuous-time Linear-Quadratic Graphon Mean Field Games
  7. 2024When is Mean-Field Reinforcement Learning Tractable and Relevant?
  8. 2025Solving Continuous Mean Field Games: Deep Reinforcement Learning for Non-Stationary Dynamics