# Learning the Globally Optimal Distributed LQ Regulator

arXiv: https://arxiv.org/abs/1912.08774 · HTML: https://mlsanity.com/paper/1912.08774/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2019.

## Built on by (most cited first, 20 of 20)

- [Derivative-Free Policy Optimization for Linear Risk-Sensitive and Robust Control Design: Implicit Regularization and Sample Complexity](https://mlsanity.com/paper/2101.01041/) (2021)
- [Revisiting LQR Control from the Perspective of Receding-Horizon Policy Gradient](https://mlsanity.com/paper/2302.13144/) (2023)
- [Learning the Kalman Filter with Fine-Grained Sample Complexity](https://mlsanity.com/paper/2301.12624/) (2023)
- [On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure](https://mlsanity.com/paper/2110.07112/) (2021)
- [Global Convergence of Direct Policy Search for State-Feedback H_∞ Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferential](https://mlsanity.com/paper/2210.11577/) (2022)
- [Regret Analysis of Distributed Online LQR Control for Unknown LTI Systems](https://mlsanity.com/paper/2105.07310/) (2021)
- [Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies](https://mlsanity.com/paper/2210.04810/) (2022)
- [Controlgym: Large-Scale Control Environments for Benchmarking Reinforcement Learning Algorithms](https://mlsanity.com/paper/2311.18736/) (2023)
- [Model-Free μ Synthesis via Adversarial Reinforcement Learning](https://mlsanity.com/paper/2111.15537/) (2021)
- [Asynchronous Distributed Reinforcement Learning for LQR Control via Zeroth-Order Block Coordinate Descent](https://mlsanity.com/paper/2107.12416/) (2021)
- [Learning Zero-Sum Linear Quadratic Games with Improved Sample Complexity and Last-Iterate Convergence](https://mlsanity.com/paper/2309.04272/) (2023)
- [Global Convergence of Receding-Horizon Policy Search in Learning Estimator Designs](https://mlsanity.com/paper/2309.04831/) (2023)
- [Optimization Landscape of Policy Gradient Methods for Discrete-time Static Output Feedback](https://mlsanity.com/paper/2310.19022/) (2023)
- [Non-Uniform Noise-to-Signal Ratio in the REINFORCE Policy-Gradient Estimator](https://mlsanity.com/paper/2602.01460/) (2026)
- [Learning Stochastic Optimal Policies via Gradient Descent](https://mlsanity.com/paper/2106.03780/) (2021)
- [Learning Decentralized Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2210.08886/) (2022)
- [Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems](https://mlsanity.com/paper/2602.22577/) (2026)
- [Accelerated Optimization Landscape of Linear-Quadratic Regulator](https://mlsanity.com/paper/2307.03590/) (2023)
- [Model-Free μ-Synthesis: A Nonsmooth Optimization Perspective](https://mlsanity.com/paper/2402.11654/) (2024)
- [A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systems](https://mlsanity.com/paper/2608.02375/) (2026)

## Abstract (arXiv)

We study model-free learning methods for the output-feedback Linear Quadratic (LQ) control problem in finite-horizon subject to subspace constraints on the control policy. Subspace constraints naturally arise in the field of distributed control and present a significant challenge in the sense that standard model-based optimization and learning leads to intractable numerical programs in general. Building upon recent results in zeroth-order optimization, we establish model-free sample-complexity bounds for the class of distributed LQ problems where a local gradient dominance constant exists on any sublevel set of the cost function. %which admit a local gradient dominance constant valid on the sublevel set of the cost function. We prove that a fundamental class of distributed control problems - commonly referred to as Quadratically Invariant (QI) problems - as well as others possess this property. To the best of our knowledge, our result is the first sample-complexity bound guarantee on learning globally optimal distributed output-feedback control policies.