mlsanityData to 14 Oct 2026

Learning Decentralized Linear Quadratic Regulators with √T Regret

arXiv 2210.08886 ↗First posted 17 Oct 2022math.OC cs.LG cs.SYcited by 1

Not on the map. Why?

Abstract (arXiv)

We propose an online learning algorithm that adaptively designs a decentralized linear quadratic regulator when the system model is unknown a priori and new data samples from a single system trajectory become progressively available. The algorithm uses a disturbance-feedback representation of state-feedback controllers coupled with online convex optimization with memory and delayed feedback. Under the assumption that the system is stable or given a known stabilizing controller, we show that our controller enjoys an expected regret that scales as √T with the time horizon T for the case of partially nested information pattern. For more general information patterns, the optimal controller is unknown even if the system model is known. In this case, the regret of our controller is shown with respect to a linear sub-optimal controller. We validate our theoretical findings using numerical experiments.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 31 of its 55 references that are in the map. First posted on arXiv 17 Oct 2022.

Builds on

31 of 55 references.

References · 31

  1. 2021Convex optimizationcited by 2,515
  2. 2013Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programmingcited by 724
  3. 2018Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulatorcited by 250
  4. 2017On the Sample Complexity of the Linear Quadratic Regulatorcited by 159
  5. 2020Naive Exploration is Optimal for Online LQRcited by 116
  6. 2019Online Control with Adversarial Disturbancescited by 92
  7. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  8. 2018Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulatorcited by 86
  9. 2020Improper Learning for Non-Stochastic Controlcited by 83
  10. 2019Learning Linear-Quadratic Regulators Efficiently with only √T Regretcited by 70
  11. 2018Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systemscited by 67
  12. 2019Policy Optimization for H2 Linear Control with H_∞ Robustness Guarantee: Implicit Regularization and Global Convergencecited by 46
19 more
  1. 2019Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problemcited by 46
  2. 2020Logarithmic Regret Bound in Partially Observable Linear Dynamical Systemscited by 46
  3. 2020Black-Box Control for Linear Dynamical Systemscited by 43
  4. 2018The Gap Between Model-Based and Model-Free Methods on the Linear Quadratic Regulator: An Asymptotic Viewpointcited by 40
  5. 2019LQR through the Lens of First Order Methods: Discrete-time Casecited by 40
  6. 2019Distributed Reinforcement Learning for Decentralized Linear Quadratic Control: A Derivative-Free Policy Optimization Approachcited by 38
  7. 2020Logarithmic Regret for Learning Linear Quadratic Regulators Efficientlycited by 35
  8. 2019Learning Sparse Dynamical Systems from a Single Sample Trajectorycited by 20
  9. 2019Learning the Globally Optimal Distributed LQ Regulatorcited by 20
  10. 2020Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systemscited by 16
  11. 2022Identifying the Dynamics of a System by Leveraging Data from Similar Systemscited by 15
  12. 2021Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regretcited by 12
  13. 2021Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guaranteescited by 11
  14. 2022Regret Lower Bounds for Learning Linear Quadratic Gaussian Systemscited by 11
  15. 2017Learning-based Control of Unknown Linear Systems with Thompson Samplingcited by 10
  16. 2021On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structurecited by 7
  17. 2022Online Adversarial Stabilization of Unknown Networked Systemscited by 5
  18. 2019On the Equivalence of Youla, System-level and Input-output Parameterizationscited by 3
  19. 2013Optimal Decentralized State-Feedback Control with Sparsity and Delayscited by 2

Built on by

Cited by year

Citing papers per year: 2024: 1.

1 paper.

  1. 2024Online Convex Optimization with Memory and Limited Predictionscited by 0