# Regularization for Covariance Parameterization of Direct Data-Driven LQR Control

arXiv: https://arxiv.org/abs/2503.02985 · HTML: https://mlsanity.com/paper/2503.02985/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2025.

## Built on by (most cited first, 4 of 4)

- [Policy Gradient Adaptive Control for the LQR: Indirect and Direct Approaches](https://mlsanity.com/paper/2505.03706/) (2025)
- [Sample-efficient and Scalable Exploration in Continuous-Time RL](https://mlsanity.com/paper/2510.24482/) (2025)
- [Optimistic Online LQR via Intrinsic Rewards](https://mlsanity.com/paper/2603.28938/) (2026)
- [Data-Driven Continuous-Time Linear Quadratic Regulator via Closed-Loop and Reinforcement Learning Parameterizations](https://mlsanity.com/paper/2604.27922/) (2026)

## Abstract (arXiv)

As the benchmark of data-driven control methods, the linear quadratic regulator (LQR) problem has gained significant attention. A growing trend is direct LQR design, which finds the optimal LQR gain directly from raw data and bypassing system identification. To achieve this, our previous work develops a direct LQR formulation parameterized by sample covariance. In this paper, we propose a regularization method for the covariance-parameterized LQR. We show that the regularizer accounts for the uncertainty in both the steady-state covariance matrix corresponding to closed-loop stability, and the LQR cost function corresponding to averaged control performance. With a positive or negative coefficient, the regularizer can be interpreted as promoting either exploitation or exploration, which are well-known trade-offs in reinforcement learning. In simulations, we observe that our covariance-parameterized LQR with regularization can significantly outperform the certainty-equivalence LQR in terms of both the optimality gap and the robust closed-loop stability.