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

arXiv: https://arxiv.org/abs/2110.07112 · HTML: https://mlsanity.com/paper/2110.07112/

## Key facts

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

## Builds on (most cited first, 22 of 22)

- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Learning Linear-Quadratic Regulators Efficiently with only √T Regret](https://mlsanity.com/paper/1902.06223/) (2019)
- [Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems](https://mlsanity.com/paper/1812.08305/) (2018)
- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [Policy Optimization for H2 Linear Control with H_∞ Robustness Guarantee: Implicit Regularization and Global Convergence](https://mlsanity.com/paper/1910.09496/) (2019)
- [Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems](https://mlsanity.com/paper/2003.11227/) (2020)
- [The Gap Between Model-Based and Model-Free Methods on the Linear Quadratic Regulator: An Asymptotic Viewpoint](https://mlsanity.com/paper/1812.03565/) (2018)
- [LQR through the Lens of First Order Methods: Discrete-time Case](https://mlsanity.com/paper/1907.08921/) (2019)
- [Distributed Reinforcement Learning for Decentralized Linear Quadratic Control: A Derivative-Free Policy Optimization Approach](https://mlsanity.com/paper/1912.09135/) (2019)
- [Logarithmic Regret for Learning Linear Quadratic Regulators Efficiently](https://mlsanity.com/paper/2002.08095/) (2020)
- [Learning Sparse Dynamical Systems from a Single Sample Trajectory](https://mlsanity.com/paper/1904.09396/) (2019)
- [Learning the Globally Optimal Distributed LQ Regulator](https://mlsanity.com/paper/1912.08774/) (2019)
- [Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems](https://mlsanity.com/paper/2011.09929/) (2020)
- [Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2102.12608/) (2021)
- [On the Equivalence of Youla, System-level and Input-output Parameterizations](https://mlsanity.com/paper/1907.06256/) (2019)
- [Optimal Decentralized State-Feedback Control with Sparsity and Delays](https://mlsanity.com/paper/1306.0036/) (2013)

## Built on by (most cited first, 7 of 7)

- [Learning Dynamical Systems by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2302.04344/) (2023)
- [Learning Linearized Models from Nonlinear Systems with Finite Data](https://mlsanity.com/paper/2309.08805/) (2023)
- [Model-Free Learning for the Linear Quadratic Regulator over Rate-Limited Channels](https://mlsanity.com/paper/2401.01258/) (2024)
- [Learning Decentralized Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2210.08886/) (2022)
- [Exploiting inter-agent coupling information for efficient reinforcement learning of cooperative LQR](https://mlsanity.com/paper/2504.20927/) (2025)
- [Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Data](https://mlsanity.com/paper/2505.04954/) (2025)
- [Communication-aware Wide-Area Damping Control using Risk-Constrained Reinforcement Learning](https://mlsanity.com/paper/2509.23620/) (2025)

## 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.