mlsanityData to 14 Oct 2026

Logarithmic Regret for Learning Linear Quadratic Regulators Efficiently

arXiv 2002.08095 ↗First posted 19 Feb 2020cs.LG stat.MLcited by 35

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Abstract (arXiv)

We consider the problem of learning in Linear Quadratic Control systems whose transition parameters are initially unknown. Recent results in this setting have demonstrated efficient learning algorithms with regret growing with the square root of the number of decision steps. We present new efficient algorithms that achieve, perhaps surprisingly, regret that scales only (poly)logarithmically with the number of steps in two scenarios: when only the state transition matrix A is unknown, and when only the state-action transition matrix B is unknown and the optimal policy satisfies a certain non-degeneracy condition. On the other hand, we give a lower bound that shows that when the latter condition is violated, square root regret is unavoidable.

Key facts. Cited by 35 papers in the map (data through 14 Oct 2026). First posted on arXiv 19 Feb 2020.

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Citing papers per year: 2021: 9; 2022: 9; 2023: 8; 2024: 4; 2025: 3; 2026: 2.

35 papers.

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  1. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 53
  2. 2021Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Boundscited by 14
  3. 2021Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regretcited by 12
  4. 2022Regret Lower Bounds for Learning Linear Quadratic Gaussian Systemscited by 11
  5. 2021Sparsity in Partially Controllable Linear Systemscited by 9
  6. 2022Thompson Sampling Achieves tilde O(√T) Regret in Linear Quadratic Controlcited by 8
  7. 2023Learning Dynamical Systems by Leveraging Data from Similar Systemscited by 8
  8. 2021On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structurecited by 7
  9. 2023Optimal Rates for Bandit Nonstochastic Controlcited by 7
  10. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  11. 2023Nonasymptotic Regret Analysis of Adaptive Linear Quadratic Control with Model Misspecificationcited by 6
  12. 2022Rate-Optimal Online Convex Optimization in Adaptive Linear Controlcited by 5
23 more
  1. 2021Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systemscited by 4
  2. 2022Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamicscited by 4
  3. 2023Sample Efficient Reinforcement Learning with Partial Dynamics Knowledgecited by 4
  4. 2024Regret Analysis of Multi-task Representation Learning for Linear-Quadratic Adaptive Controlcited by 4
  5. 2024Model-Free Learning for the Linear Quadratic Regulator over Rate-Limited Channelscited by 2
  6. 2025Convergence Guarantees of Model-free Policy Gradient Methods for LQR with Stochastic Datacited by 2
  7. 2022Learning Decentralized Linear Quadratic Regulators with √T Regretcited by 1
  8. 2023Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbancescited by 1
  9. 2023On the Hardness of Learning to Stabilize Linear Systemscited by 1
  10. 2023Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guaranteescited by 1
  11. 2024Stability-Certified On-Policy Data-Driven LQR via Recursive Learning and Policy Gradientcited by 1
  12. 2025Adversarially Robust Multitask Adaptive Controlcited by 1
  13. 2021Improper Reinforcement Learning with Gradient-based Policy Optimizationcited by 0
  14. 2021Safe Linear-Quadratic Dual Control with Almost Sure Performance Guaranteecited by 0
  15. 2021Reinforcement Learning Policies in Continuous-Time Linear Systemscited by 0
  16. 2022Rate-matching the regret lower-bound in the linear quadratic regulator with unknown dynamicscited by 0
  17. 2022Learning to Control under Time-Varying Environmentcited by 0
  18. 2022Regret Analysis of Certainty Equivalence Policies in Continuous-Time Linear-Quadratic Systemscited by 0
  19. 2023Finite Time Regret Bounds for Minimum Variance Control of Autoregressive Systems with Exogenous Inputscited by 0
  20. 2024Online Control of Linear Systems under Unbounded Noisecited by 0
  21. 2025Logarithmic Regret for Nonlinear Controlcited by 0
  22. 2026Online Nonstochastic Prediction: Logarithmic Regret via Predictive Online Least Squarescited by 0
  23. 2026A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systemscited by 0