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Learning Linear-Quadratic Regulators Efficiently with only √T Regret

arXiv 1902.06223 ↗First posted 17 Feb 2019cs.LG stat.MLcited by 70

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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).

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

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Citing papers per year: 2021: 18; 2022: 13; 2023: 9; 2024: 12; 2025: 10; 2026: 8.

70 papers.

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  1. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 53
  2. 2021Stabilizing Dynamical Systems via Policy Gradient Methodscited by 25
  3. 2021A Free Lunch from the Noise: Provable and Practical Exploration for Representation Learningcited by 24
  4. 2023Optimal Exploration for Model-Based RL in Nonlinear Systemscited by 18
  5. 2021Lazy OCO: Online Convex Optimization on a Switching Budgetcited by 14
  6. 2021PC-MLP: Model-based Reinforcement Learning with Policy Cover Guided Explorationcited by 14
  7. 2023Rate-Optimal Policy Optimization for Linear Markov Decision Processescited by 14
  8. 2022Online Control of Unknown Time-Varying Dynamical Systemscited by 13
  9. 2021Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regretcited by 12
  10. 2024Sublinear Regret for a Class of Continuous-Time Linear-Quadratic Reinforcement Learning Problemscited by 12
  11. 2025Optimistically Optimistic Exploration for Provably Efficient Infinite-Horizon Reinforcement and Imitation Learningcited by 12
  12. 2022Regret Lower Bounds for Learning Linear Quadratic Gaussian Systemscited by 11
38 more
  1. 2021Regret-optimal Estimation and Controlcited by 10
  2. 2024Near-Optimal Regret in Linear MDPs with Aggregate Bandit Feedbackcited by 10
  3. 2021Sparsity in Partially Controllable Linear Systemscited by 9
  4. 2022Global Convergence of Two-timescale Actor-Critic for Solving Linear Quadratic Regulatorcited by 8
  5. 2021On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structurecited by 7
  6. 2025SOMBRL: Scalable and Optimistic Model-Based RLcited by 7
  7. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  8. 2022Optimal scheduling of entropy regulariser for continuous-time linear-quadratic reinforcement learningcited by 6
  9. 2022Best of Both Worlds in Online Control: Competitive Ratio and Policy Regretcited by 6
  10. 2023Nonasymptotic Regret Analysis of Adaptive Linear Quadratic Control with Model Misspecificationcited by 6
  11. 2024No-Regret Reinforcement Learning in Smooth MDPscited by 6
  12. 2025The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspectivecited by 6
  13. 2025Universal Sequence Preconditioningcited by 6
  14. 2021Regret Analysis of Learning-Based MPC with Partially-Unknown Cost Functioncited by 5
  15. 2021Exponential Family Model-Based Reinforcement Learning via Score Matchingcited by 5
  16. 2022Rate-Optimal Online Convex Optimization in Adaptive Linear Controlcited by 5
  17. 2022Meta-Learning Online Control for Linear Dynamical Systemscited by 5
  18. 2024Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPscited by 5
  19. 2025IL-SOAR : Imitation Learning with Soft Optimistic Actor cRiticcited by 5
  20. 2025Policy Gradient Adaptive Control for the LQR: Indirect and Direct Approachescited by 5
  21. 2021Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systemscited by 4
  22. 2022Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamicscited by 4
  23. 2024NeoRL: Efficient Exploration for Nonepisodic RLcited by 4
  24. 2024Regret Analysis of Multi-task Representation Learning for Linear-Quadratic Adaptive Controlcited by 4
  25. 2024Local Linearity: the Key for No-regret Reinforcement Learning in Continuous MDPscited by 4
  26. 2021Online Learning for Predictive Control with Provable Regret Guaranteescited by 3
  27. 2024Combining Federated Learning and Control: A Surveycited by 3
  28. 2021Scalable regret for learning to control network-coupled subsystems with unknown dynamicscited by 2
  29. 2022Optimal Competitive-Ratio Controlcited by 2
  30. 2023Near-continuous time Reinforcement Learning for continuous state-action spacescited by 2
  31. 2023Best of Both Worlds Guarantees for Smoothed Online Quadratic Optimizationcited by 2
  32. 2024Learning to Stabilize Unknown LTI Systems on a Single Trajectory under Stochastic Noisecited by 2
  33. 2025A New Approach to Controlling Linear Dynamical Systemscited by 2
  34. 2025Global Optimality of Single-Timescale Actor-Critic under Continuous State-Action Space: A Study on Linear Quadratic Regulatorcited by 2
  35. 2021A relaxed technical assumption for posterior sampling-based reinforcement learning for control of unknown linear systemscited by 1
  36. 2022Learning Decentralized Linear Quadratic Regulators with √T Regretcited by 1
  37. 2023Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbancescited by 1
  38. 2023On the Hardness of Learning to Stabilize Linear Systemscited by 1

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