mlsanityData to 7 Oct 2026

Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQR

arXiv 2401.14534 ↗First posted 25 Jan 2024math.OC cs.LGcited by 14

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Abstract (arXiv)

We investigate the problem of learning linear quadratic regulators (LQR) in a multi-task, heterogeneous, and model-free setting. We characterize the stability and personalization guarantees of a policy gradient-based (PG) model-agnostic meta-learning (MAML) (Finn et al., 2017) approach for the LQR problem under different task-heterogeneity settings. We show that our MAML-LQR algorithm produces a stabilizing controller close to each task-specific optimal controller up to a task-heterogeneity bias in both model-based and model-free learning scenarios. Moreover, in the model-based setting, we show that such a controller is achieved with a linear convergence rate, which improves upon sub-linear rates from existing work. Our theoretical guarantees demonstrate that the learned controller can efficiently adapt to unseen LQR tasks.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 24 of its 43 references that are in the map. First posted on arXiv 25 Jan 2024.

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24 of 43 references.

References · 24

  1. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,861
  2. 2016RL2: Fast Reinforcement Learning via Slow Reinforcement Learningcited by 490
  3. 2016Learning to reinforcement learncited by 369
  4. 2018Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulatorcited by 211
  5. 2019Online Meta-Learningcited by 137
  6. 2019On the Convergence Theory of Gradient-Based Model-Agnostic Meta-Learning Algorithmscited by 132
  7. 2023A Tutorial on Meta-Reinforcement Learningcited by 102
  8. 2018ProMP: Proximal Meta-Policy Searchcited by 91
  9. 2022Sharp-MAML: Sharpness-Aware Model-Agnostic Meta Learningcited by 57
  10. 2018Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systemscited by 56
  11. 2019LQR through the Lens of First Order Methods: Discrete-time Casecited by 30
  12. 2021Stabilizing Dynamical Systems via Policy Gradient Methodscited by 24
12 more
  1. 2022Multi-Task Imitation Learning for Linear Dynamical Systemscited by 22
  2. 2020On the Convergence Theory of Debiased Model-Agnostic Meta-Reinforcement Learningcited by 19
  3. 2023Model-free Learning with Heterogeneous Dynamical Systems: A Federated LQR Approachcited by 19
  4. 2022Control-oriented meta-learningcited by 17
  5. 2022FedSysID: A Federated Approach to Sample-Efficient System Identificationcited by 15
  6. 2023Sample-Efficient Linear Representation Learning from Non-IID Non-Isotropic Datacited by 12
  7. 2021A Theoretical Understanding of Gradient Bias in Meta-Reinforcement Learningcited by 11
  8. 2023Learning Personalized Models with Clustered System Identificationcited by 10
  9. 2020Zeroth-Order Feedback Optimization for Cooperative Multi-Agent Systemscited by 6
  10. 2023Multi-Task System Identification of Similar Linear Time-Invariant Dynamical Systemscited by 6
  11. 2023Convergence of Gradient-based MAML in LQRcited by 5
  12. 2023Oracle Complexity Reduction for Model-free LQR: A Stochastic Variance-Reduced Policy Gradient Approachcited by 1

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Citing papers per year: 2024: 5; 2025: 7; 2026: 2.

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