mlsanityData to 14 Oct 2026

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

arXiv 2608.30244 ↗First posted 31 Aug 2026math.OCcited by 0

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

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.

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.

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20 of 51 references.

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

Other references · 19

  1. 2020Fictitious Play for Mean Field Games: Continuous Time Analysis and Applicationscited by 62
  2. 2020Entropy Regularization for Mean Field Games with Learningcited by 58
  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. 2020Breaking the Curse of Many Agents: Provable Mean Embedding Q-Iteration for Mean-Field Reinforcement Learningcited by 21
  6. 2020Robust Policy Iteration for Continuous-time Linear Quadratic Regulationcited by 15
  7. 2020Graphon Mean Field Games and the GMFG Equationscited by 13
  8. 2016Proximal methods for stationary Mean Field Games with local couplingscited by 11
  9. 2022Graphon Mean-Field Control for Cooperative Multi-Agent Reinforcement Learningcited by 11
  10. 2022Robust Reinforcement Learning for Risk-Sensitive Linear Quadratic Gaussian Controlcited by 7
  11. 2017Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamicscited by 6
  12. 2014Linear-Quadratic N-person and Mean-Field Games with Ergodic Costcited by 5
7 more
  1. 2017Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown L2-Disturbancecited by 4
  2. 2018On the convergence of closed-loop Nash equilibria to the mean field game limitcited by 4
  3. 2020Linear quadratic mean field social optimization: Asymptotic solvability and decentralized controlcited by 4
  4. 2023Policy Iteration Reinforcement Learning Method for Continuous-Time Linear-Quadratic Mean-Field Control Problemscited by 4
  5. 2020Mean Field Linear Quadratic Control: Uniform Stabilization and Social Optimalitycited by 3
  6. 2022Decentralized Strategies for Finite Population Linear-Quadratic-Gaussian Games and Teamscited by 1
  7. 2024Linear-Quadratic Mean-Field Game for Stochastic Systems with Partial Observationcited by 1

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  3. 2026Inverse reinforcement learning for indefinite mean-field social optimization with multiplicative noise
  4. 2025Data-Driven Mean Field Equilibrium Computation in Large-Population LQG Games
  5. 2024Scalable Reinforcement Learning for Linear-Quadratic Control of Networks
  6. 2025Model-free stochastic linear quadratic control for discrete-time systems with multiplicative and additive noises via semidefinite programming
  7. 2024Full error analysis of policy gradient learning algorithms for exploratory linear quadratic mean-field control problem in continuous time with common noise
  8. 2026Reinforcement Learning Method for Zero-Sum Linear-Quadratic Stochastic Differential Games in Infinite Horizons