mlsanityData to 7 Oct 2026

On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure

arXiv 2110.07112 ↗First posted 14 Oct 2021math.OC cs.LG cs.SYcited by 7

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Abstract (arXiv)

We study the problem of control policy design for decentralized state-feedback linear quadratic control with a partially nested information structure, when the system model is unknown. We propose a model-based learning solution, which consists of two steps. First, we estimate the unknown system model from a single system trajectory of finite length, using least squares estimation. Next, based on the estimated system model, we design a control policy that satisfies the desired information structure. We show that the suboptimality gap between our control policy and the optimal decentralized control policy (designed using accurate knowledge of the system model) scales linearly with the estimation error of the system model. Using this result, we provide an end-to-end sample complexity result for learning decentralized controllers for a linear quadratic control problem with a partially nested information structure.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 22 of its 48 references that are in the map. First posted on arXiv 14 Oct 2021.

Builds on

22 of 48 references.

References · 22

  1. 2013Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programmingcited by 716
  2. 2018Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulatorcited by 211
  3. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  4. 2017On the Sample Complexity of the Linear Quadratic Regulatorcited by 151
  5. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  6. 2018Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulatorcited by 86
  7. 2020Improper Learning for Non-Stochastic Controlcited by 83
  8. 2019Learning Linear-Quadratic Regulators Efficiently with only √T Regretcited by 67
  9. 2017Finite Time Identification in Unstable Linear Systemscited by 66
  10. 2018Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systemscited by 56
  11. 2020Logarithmic Regret Bound in Partially Observable Linear Dynamical Systemscited by 46
  12. 2019Policy Optimization for H2 Linear Control with H_∞ Robustness Guarantee: Implicit Regularization and Global Convergencecited by 39
10 more
  1. 2018The Gap Between Model-Based and Model-Free Methods on the Linear Quadratic Regulator: An Asymptotic Viewpointcited by 36
  2. 2019Distributed Reinforcement Learning for Decentralized Linear Quadratic Control: A Derivative-Free Policy Optimization Approachcited by 33
  3. 2020Logarithmic Regret for Learning Linear Quadratic Regulators Efficientlycited by 33
  4. 2019LQR through the Lens of First Order Methods: Discrete-time Casecited by 30
  5. 2019Learning Sparse Dynamical Systems from a Single Sample Trajectorycited by 20
  6. 2019Learning the Globally Optimal Distributed LQ Regulatorcited by 19
  7. 2020Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systemscited by 15
  8. 2021Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regretcited by 10
  9. 2019On the Equivalence of Youla, System-level and Input-output Parameterizationscited by 3
  10. 2013Optimal Decentralized State-Feedback Control with Sparsity and Delayscited by 2

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Cited by year

Citing papers per year: 2022: 1; 2023: 2; 2024: 1; 2025: 3.

7 papers.

  1. 2023Learning Dynamical Systems by Leveraging Data from Similar Systemscited by 8
  2. 2023Learning Linearized Models from Nonlinear Systems with Finite Datacited by 3
  3. 2022Learning Decentralized Linear Quadratic Regulators with √T Regretcited by 1
  4. 2024Model-Free Learning for the Linear Quadratic Regulator over Rate-Limited Channelscited by 1
  5. 2025Exploiting inter-agent coupling information for efficient reinforcement learning of cooperative LQRcited by 1
  6. 2025Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Datacited by 1
  7. 2025Communication-aware Wide-Area Damping Control using Risk-Constrained Reinforcement Learningcited by 0