# On the Sample Complexity of the Linear Quadratic Gaussian Regulator

arXiv: https://arxiv.org/abs/2304.00381 · HTML: https://mlsanity.com/paper/2304.00381/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [Optimal Exploration for Model-Based RL in Nonlinear Systems](https://mlsanity.com/paper/2306.09210/) (2023)

## Abstract (arXiv)

In this paper we provide direct data-driven expressions for the Linear Quadratic Regulator (LQR), the Kalman filter, and the Linear Quadratic Gaussian (LQG) controller using a finite dataset of noisy input, state, and output trajectories. We show that our data-driven expressions are consistent, since they converge as the number of experimental trajectories increases, we characterize their convergence rate, and quantify their error as a function of the system and data properties. These results complement the body of literature on data-driven control and finite-sample analysis, and provide new ways to solve canonical control and estimation problems that do not assume, nor require the estimation of, a model of the system and noise and do not rely on solving implicit equations.