# Data-enabled Policy Optimization for the Linear Quadratic Regulator

arXiv: https://arxiv.org/abs/2303.17958 · HTML: https://mlsanity.com/paper/2303.17958/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2023.

## Built on by (most cited first, 3 of 3)

- [Policy Gradient Adaptive Control for the LQR: Indirect and Direct Approaches](https://mlsanity.com/paper/2505.03706/) (2025)
- [Implicit Bias of Policy Gradient in Linear Quadratic Control: Extrapolation to Unseen Initial States](https://mlsanity.com/paper/2402.07875/) (2024)
- [Data-Driven Continuous-Time Linear Quadratic Regulator via Closed-Loop and Reinforcement Learning Parameterizations](https://mlsanity.com/paper/2604.27922/) (2026)

## Abstract (arXiv)

Policy optimization (PO), an essential approach of reinforcement learning for a broad range of system classes, requires significantly more system data than indirect (identification-followed-by-control) methods or behavioral-based direct methods even in the simplest linear quadratic regulator (LQR) problem. In this paper, we take an initial step towards bridging this gap by proposing the data-enabled policy optimization (DeePO) method, which requires only a finite number of sufficiently exciting data to iteratively solve the LQR problem via PO. Based on a data-driven closed-loop parameterization, we are able to directly compute the policy gradient from a batch of persistently exciting data. Next, we show that the nonconvex PO problem satisfies a projected gradient dominance property by relating it to an equivalent convex program, leading to the global convergence of DeePO. Moreover, we apply regularization methods to enhance certainty-equivalence and robustness of the resulting controller and show an implicit regularization property. Finally, we perform simulations to validate our results.