# Low-complexity Learning of Linear Quadratic Regulators from Noisy Data

arXiv: https://arxiv.org/abs/2005.01082 · HTML: https://mlsanity.com/paper/2005.01082/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2020.

## Built on by (most cited first, 8 of 8)

- [Stability-Certified On-Policy Data-Driven LQR via Recursive Learning and Policy Gradient](https://mlsanity.com/paper/2403.05367/) (2024)
- [Data-Driven Motion Planning for Uncertain Nonlinear Systems](https://mlsanity.com/paper/2508.00154/) (2025)
- [Data-Driven Adversarial Online Control for Unknown Linear Systems](https://mlsanity.com/paper/2308.08138/) (2023)
- [MR-ARL: Model Reference Adaptive Reinforcement Learning for Robustly Stable On-Policy Data-Driven LQR](https://mlsanity.com/paper/2402.14483/) (2024)
- [Regret Analysis of Policy Optimization over Submanifolds for Linearly Constrained Online LQG](https://mlsanity.com/paper/2403.08553/) (2024)
- [Direct Data Driven Control Using Noisy Measurements](https://mlsanity.com/paper/2505.06407/) (2025)
- [Risk-Aware Safe Reinforcement Learning for Control of Stochastic Linear Systems](https://mlsanity.com/paper/2505.09734/) (2025)
- [Data-Driven Continuous-Time Linear Quadratic Regulator via Closed-Loop and Reinforcement Learning Parameterizations](https://mlsanity.com/paper/2604.27922/) (2026)

## Abstract (arXiv)

This paper considers the Linear Quadratic Regulator problem for linear systems with unknown dynamics, a central problem in data-driven control and reinforcement learning. We propose a method that uses data to directly return a controller without estimating a model of the system. Sufficient conditions are given under which this method returns a stabilizing controller with guaranteed relative error when the data used to design the controller are affected by noise. This method has low complexity as it only requires a finite number of samples of the system response to a sufficiently exciting input, and can be efficiently implemented as a semi-definite program. Further, the method does not require assumptions on the noise statistics, and the relative error nicely scales with the noise magnitude.