# Revisiting LQR Control from the Perspective of Receding-Horizon Policy Gradient

## TL;DR

This paper analyzes the discrete-time LQR problem using receding-horizon policy gradient, providing sample complexity bounds and demonstrating the method's effectiveness in control and estimation without prior stabilizing policies.

## Contribution

It offers a detailed sample complexity analysis of RHPG for LQR, showing it can learn near-optimal policies without needing an initial stabilizing control.

## Key findings

- RHPG can learn stabilizing policies close to optimal without initial stabilizing control.
- The analysis applies to both control and estimation problems in linear systems.
- The method demonstrates broad applicability and streamlined analysis in linear control tasks.

## Abstract

We revisit in this paper the discrete-time linear quadratic regulator (LQR) problem from the perspective of receding-horizon policy gradient (RHPG), a newly developed model-free learning framework for control applications. We provide a fine-grained sample complexity analysis for RHPG to learn a control policy that is both stabilizing and $\epsilon$-close to the optimal LQR solution, and our algorithm does not require knowing a stabilizing control policy for initialization. Combined with the recent application of RHPG in learning the Kalman filter, we demonstrate the general applicability of RHPG in linear control and estimation with streamlined analyses.