Reinforcement Learning for Discrete-time LQG Mean Field Social Control Problems with Unknown Dynamics
On the map: Deep reinforcement learning methods → RL for games and combinatorial optimization
Abstract (arXiv)
This paper studies the discrete-time linear-quadratic-Gaussian mean field (MF) social control problem in an infinite horizon, where the dynamics of all agents are unknown. The objective is to design a reinforcement learning (RL) algorithm to approximate the decentralized asymptotic optimal social control in terms of two algebraic Riccati equations (AREs). In this problem, a coupling term is introduced into the system dynamics to capture the interactions among agents. This causes the equivalence between model-based and model-free methods to be invalid, which makes it difficult to directly apply traditional model-free algorithms. Firstly, under the assumptions of system stabilizability and detectability, a model-based policy iteration algorithm is proposed to approximate the stabilizing solution of the AREs. The algorithm is proven to be convergent in both cases of semi-positive definite and indefinite weight matrices. Subsequently, by adopting the method of system transformation, a model-free RL algorithm is designed to solve for asymptotic optimal social control. During the iteration process, the updates are performed using data collected from any two agents and MF state. Finally, a numerical case is provided to verify the effectiveness of the proposed algorithm.
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 13 of its 50 references that are in the map. First posted on arXiv 2 Jul 2025.
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- 2021Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learningcited by 73
- 2020Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysiscited by 49
- 2020Unified Reinforcement Q-Learning for Mean Field Game and Control Problemscited by 49
- 2019On the Convergence of Model Free Learning in Mean Field Gamescited by 48
- 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 38
- 2018On the convergence of closed-loop Nash equilibria to the mean field game limitcited by 4
- 2019Linear quadratic mean field games: Asymptotic solvability and relation to the fixed point approachcited by 3
- 2020Robust Mean Field Social Control Problems with Applications in Analysis of Opinion Dynamicscited by 3
- 2020Mean Field Linear Quadratic Control: Uniform Stabilization and Social Optimalitycited by 3
- 2016Dynamic Collective Choice: Social Optimacited by 2
- 2018Semi-Explicit Solutions to some Non-Linear Non-Quadratic Mean-Field-Type Games: A Direct Methodcited by 1
- 2020LQG Mean Field Games with a Major Agent: Nash Certainty Equivalence versus Probabilistic Approachcited by 1
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- 2026Data-Driven Network LQG Mean Field Games with Heterogeneous Populations via Integral Reinforcement Learning
- 2024Full error analysis of policy gradient learning algorithms for exploratory linear quadratic mean-field control problem in continuous time with common noise
- 2024Robust policy iteration for continuous-time stochastic H_∞ control problem with unknown dynamics
- 2026Mean Field Reinforcement Learning