# Learning Linear-Quadratic Regulators Efficiently with only √T Regret

arXiv: https://arxiv.org/abs/1902.06223 · HTML: https://mlsanity.com/paper/1902.06223/

## Key facts

- Cited by 70 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2019.

## Built on by (most cited first, 30 of 70)

- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [Stabilizing Dynamical Systems via Policy Gradient Methods](https://mlsanity.com/paper/2110.06418/) (2021)
- [A Free Lunch from the Noise: Provable and Practical Exploration for Representation Learning](https://mlsanity.com/paper/2111.11485/) (2021)
- [Optimal Exploration for Model-Based RL in Nonlinear Systems](https://mlsanity.com/paper/2306.09210/) (2023)
- [Lazy OCO: Online Convex Optimization on a Switching Budget](https://mlsanity.com/paper/2102.03803/) (2021)
- [PC-MLP: Model-based Reinforcement Learning with Policy Cover Guided Exploration](https://mlsanity.com/paper/2107.07410/) (2021)
- [Rate-Optimal Policy Optimization for Linear Markov Decision Processes](https://mlsanity.com/paper/2308.14642/) (2023)
- [Online Control of Unknown Time-Varying Dynamical Systems](https://mlsanity.com/paper/2202.07890/) (2022)
- [Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2102.12608/) (2021)
- [Sublinear Regret for a Class of Continuous-Time Linear-Quadratic Reinforcement Learning Problems](https://mlsanity.com/paper/2407.17226/) (2024)
- [Optimistically Optimistic Exploration for Provably Efficient Infinite-Horizon Reinforcement and Imitation Learning](https://mlsanity.com/paper/2502.13900/) (2025)
- [Regret Lower Bounds for Learning Linear Quadratic Gaussian Systems](https://mlsanity.com/paper/2201.01680/) (2022)
- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [Near-Optimal Regret in Linear MDPs with Aggregate Bandit Feedback](https://mlsanity.com/paper/2405.07637/) (2024)
- [Sparsity in Partially Controllable Linear Systems](https://mlsanity.com/paper/2110.06150/) (2021)
- [Global Convergence of Two-timescale Actor-Critic for Solving Linear Quadratic Regulator](https://mlsanity.com/paper/2208.08744/) (2022)
- [On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure](https://mlsanity.com/paper/2110.07112/) (2021)
- [SOMBRL: Scalable and Optimistic Model-Based RL](https://mlsanity.com/paper/2511.20066/) (2025)
- [Regret Analysis of Distributed Online LQR Control for Unknown LTI Systems](https://mlsanity.com/paper/2105.07310/) (2021)
- [Optimal scheduling of entropy regulariser for continuous-time linear-quadratic reinforcement learning](https://mlsanity.com/paper/2208.04466/) (2022)
- [Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret](https://mlsanity.com/paper/2211.11219/) (2022)
- [Nonasymptotic Regret Analysis of Adaptive Linear Quadratic Control with Model Misspecification](https://mlsanity.com/paper/2401.00073/) (2023)
- [No-Regret Reinforcement Learning in Smooth MDPs](https://mlsanity.com/paper/2402.03792/) (2024)
- [The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspective](https://mlsanity.com/paper/2501.15910/) (2025)
- [Universal Sequence Preconditioning](https://mlsanity.com/paper/2502.06545/) (2025)
- [Regret Analysis of Learning-Based MPC with Partially-Unknown Cost Function](https://mlsanity.com/paper/2108.02307/) (2021)
- [Exponential Family Model-Based Reinforcement Learning via Score Matching](https://mlsanity.com/paper/2112.14195/) (2021)
- [Rate-Optimal Online Convex Optimization in Adaptive Linear Control](https://mlsanity.com/paper/2206.01426/) (2022)
- [Meta-Learning Online Control for Linear Dynamical Systems](https://mlsanity.com/paper/2208.10259/) (2022)
- [Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPs](https://mlsanity.com/paper/2405.06363/) (2024)

## Abstract (arXiv)

We present the first computationally-efficient algorithm with widetilde O(√T) regret for learning in Linear Quadratic Control systems with unknown dynamics. By that, we resolve an open question of Abbasi-Yadkori and Szepesv'ari (2011) and Dean, Mania, Matni, Recht, and Tu (2018).