mlsanityData to 14 Oct 2026

Inverse reinforcement learning for indefinite mean-field social optimization with multiplicative noise

arXiv 2608.07252 ↗First posted 7 Aug 2026math.OCcited by 0

On the map: Deep reinforcement learning methods → RL for robot locomotion and manipulation

Abstract (arXiv)

This paper studies the inverse reinforcement learning (RL) problem for linear-quadratic mean-field (MF) social optimization. The considered system features multiplicative noise and indefinite cost weights, which violate standard convexity assumptions and pose analytical challenges. The goal is to recover unknown social cost weights from expert demonstrations and reproduce the optimal control policies. This requires solving coupled stochastic algebraic Riccati equations and Lyapunov equations with unknown system dynamics. To this end, we first propose a model-based inverse RL algorithm with two sequential loops that separately handle individual and MF dynamics, and we prove its convergence and closed-loop stabilizability. Moreover, we characterize the non-uniqueness of the recovered cost weights. To eliminate reliance on system dynamics, we develop a model-free inverse RL algorithm using integral RL and least-squares identification, which requires only measured trajectory data satisfying mild rank conditions. Finally, numerical simulations validate the effectiveness of the proposed approaches.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods. Builds on 6 of its 38 references that are in the map. First posted on arXiv 7 Aug 2026.

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6 of 38 references.

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Same direction, newest first

  1. 2024Inverse reinforcement learning by expert imitation for the stochastic linear-quadratic optimal control problem27 May

Other references · 5

  1. 2019Social Optima in Robust Mean Field LQG Control: From Finite to Infinite Horizoncited by 4
  2. 2020Indefinite Linear Quadratic Mean Field Social Control Problems with Multiplicative Noisecited by 3
  3. 2018Mean Field Production Output Control with Sticky Prices: Nash and Social Solutionscited by 2
  4. 2019Social Optima in Mean Field Linear-Quadratic-Gaussian Control with Volatility Uncertaintycited by 2
  5. 2024Comparison of two mean-field approaches to modeling an epidemic spreadcited by 1

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  3. 2025Reinforcement Learning for Discrete-time LQG Mean Field Social Control Problems with Unknown Dynamics
  4. 2026Inverse Optimal Control for Linear Quadratic Problem with Poisson Jumps: Model-Free Inverse Reinforcement Learning Approaches
  5. 2026Data-Driven Inverse Reinforcement Learning of Linear Systems with Model Uncertainty: A Convex Optimization View
  6. 2026Maximum Entropy Inverse Reinforcement Learning for Mean-Field Games with Average Reward
  7. 2024Maximum Causal Entropy IRL in Mean-Field Games and GNEP Framework for Forward RL
  8. 2025Offline Reinforcement Learning via Inverse Optimization