mlsanityData to 7 Oct 2026

Online Linear Quadratic Control

arXiv 1806.07104 ↗First posted 19 Jun 2018cs.LG stat.MLcited by 55

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Abstract (arXiv)

We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee O(√T) regret under mild assumptions, where T is the time horizon. Our algorithms rely on a novel SDP relaxation for the steady-state distribution of the system. Crucially, and in contrast to previously proposed relaxations, the feasible solutions of our SDP all correspond to "strongly stable" policies that mix exponentially fast to a steady state.

Key facts. Cited by 55 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Jun 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 16; 2022: 10; 2023: 10; 2024: 9; 2025: 7; 2026: 3.

55 papers.

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  1. 2021Non-stationary Online Learning with Memory and Non-stochastic Controlcited by 33
  2. 2021Meta-Adaptive Nonlinear Control: Theory and Algorithmscited by 23
  3. 2021Streaming Linear System Identification with Reverse Experience Replaycited by 17
  4. 2022Learning Mixtures of Linear Dynamical Systemscited by 15
  5. 2021Adversarial Tracking Control via Strongly Adaptive Online Learning with Memorycited by 14
  6. 2021Lazy OCO: Online Convex Optimization on a Switching Budgetcited by 14
  7. 2021Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Boundscited by 13
  8. 2021Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regretcited by 10
  9. 2022Learning to Control Linear Systems can be Hardcited by 10
  10. 2024Sublinear Regret for a Class of Continuous-Time Linear-Quadratic Reinforcement Learning Problemscited by 10
  11. 2022Provable Sim-to-real Transfer in Continuous Domain with Partial Observationscited by 9
  12. 2023Smoothed Online Learning for Prediction in Piecewise Affine Systemscited by 9
38 more
  1. 2021A Regret Minimization Approach to Iterative Learning Controlcited by 8
  2. 2022Thompson Sampling Achieves tilde O(√T) Regret in Linear Quadratic Controlcited by 8
  3. 2023Optimal Rates for Bandit Nonstochastic Controlcited by 7
  4. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  5. 2022Optimal Dynamic Regret in LQR Controlcited by 6
  6. 2025Universal Sequence Preconditioningcited by 6
  7. 2022Rate-Optimal Online Convex Optimization in Adaptive Linear Controlcited by 5
  8. 2022Meta-Learning Online Control for Linear Dynamical Systemscited by 5
  9. 2022Best of Both Worlds in Online Control: Competitive Ratio and Policy Regretcited by 5
  10. 2023Online Nonstochastic Control with Adversarial and Static Constraintscited by 5
  11. 2023Oracle-Efficient Smoothed Online Learning for Piecewise Continuous Decision Makingcited by 5
  12. 2025The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspectivecited by 5
  13. 2021Robust Online Control with Model Misspecificationcited by 4
  14. 2021Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systemscited by 4
  15. 2021Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systemscited by 4
  16. 2022Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamicscited by 4
  17. 2023A Nonstochastic Control Approach to Optimizationcited by 4
  18. 2021Stable Online Control of Linear Time-Varying Systemscited by 3
  19. 2021Online Learning for Predictive Control with Provable Regret Guaranteescited by 3
  20. 2022Implications of Regret on Stability of Linear Dynamical Systemscited by 3
  21. 2023Adaptive Online Non-stochastic Controlcited by 3
  22. 2024Optimistic Online Non-stochastic Control via FTRLcited by 3
  23. 2024Combining Federated Learning and Control: A Surveycited by 2
  24. 2025A New Approach to Controlling Linear Dynamical Systemscited by 2
  25. 2025Sample and Computationally Efficient Continuous-Time Reinforcement Learning with General Function Approximationcited by 2
  26. 2021On the Effectiveness of Iterative Learning Controlcited by 1
  27. 2023Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based controlcited by 1
  28. 2023Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbancescited by 1
  29. 2024The Complexity of Sequential Prediction in Dynamical Systemscited by 1
  30. 2024Optimistic Safety for Online Convex Optimization with Unknown Linear Constraintscited by 1
  31. 2024Online Stackelberg Optimization via Nonlinear Controlcited by 1
  32. 2025The Confusing Instance Principle for Online Linear Quadratic Controlcited by 1
  33. 2021Differentiable Robust LQR Layerscited by 0
  34. 2023Regret Analysis of Online LQR Control via Trajectory Prediction and Tracking: Extended Versioncited by 0
  35. 2023Online Decision Making with History-Average Dependent Costs (Extended)cited by 0
  36. 2024Online Control of Linear Systems under Unbounded Noisecited by 0
  37. 2024Regret Analysis of Policy Optimization over Submanifolds for Linearly Constrained Online LQGcited by 0
  38. 2024Differentiable Quantum Computing for Large-scale Linear Controlcited by 0

50 most cited of 55 All 55 (JSON)