mlsanityData to 7 Oct 2026

Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator

arXiv 1805.09388 ↗First posted 23 May 2018cs.LG math.OC stat.MLcited by 86

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Abstract (arXiv)

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

Key facts. Cited by 86 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 May 2018.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 25; 2022: 18; 2023: 19; 2024: 10; 2025: 9; 2026: 4.

86 papers.

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  1. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 52
  2. 2021Statistical Inference with M-Estimators on Adaptively Collected Datacited by 40
  3. 2021Stabilizing Dynamical Systems via Policy Gradient Methodscited by 24
  4. 2021Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controlscited by 21
  5. 2019On the Global Convergence of Imitation Learning: A Case for Linear Quadratic Regulatorcited by 20
  6. 2021Online Learning for Unknown Partially Observable MDPscited by 17
  7. 2023Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEscited by 16
  8. 2021Task-Optimal Exploration in Linear Dynamical Systemscited by 15
  9. 2021PC-MLP: Model-based Reinforcement Learning with Policy Cover Guided Explorationcited by 14
  10. 2023Butterfly Effects of SGD Noise: Error Amplification in Behavior Cloning and Autoregressioncited by 14
  11. 2021Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Boundscited by 13
  12. 2022Online Control of Unknown Time-Varying Dynamical Systemscited by 13
38 more
  1. 2022Finite Sample Identification of Bilinear Dynamical Systemscited by 12
  2. 2023Sample-Efficient Linear Representation Learning from Non-IID Non-Isotropic Datacited by 12
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  5. 2021Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guaranteescited by 10
  6. 2022Learning to Control Linear Systems can be Hardcited by 10
  7. 2021A Regret Minimization Approach to Iterative Learning Controlcited by 8
  8. 2022Thompson Sampling Achieves tilde O(√T) Regret in Linear Quadratic Controlcited by 8
  9. 2022Global Convergence of Two-timescale Actor-Critic for Solving Linear Quadratic Regulatorcited by 8
  10. 2023Learning Dynamical Systems by Leveraging Data from Similar Systemscited by 8
  11. 2021Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertaintycited by 7
  12. 2021On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structurecited by 7
  13. 2023Optimal Rates for Bandit Nonstochastic Controlcited by 7
  14. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  15. 2021Provable Regret Bounds for Deep Online Learning and Controlcited by 6
  16. 2022Online Convex Optimization with Unbounded Memorycited by 6
  17. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  18. 2023On Representation Complexity of Model-based and Model-free Reinforcement Learningcited by 6
  19. 2023Nonasymptotic Regret Analysis of Adaptive Linear Quadratic Control with Model Misspecificationcited by 6
  20. 2024No-Regret Reinforcement Learning in Smooth MDPscited by 6
  21. 2024Learning Linear Dynamics from Bilinear Observationscited by 6
  22. 2025Universal Sequence Preconditioningcited by 6
  23. 2021Exponential Family Model-Based Reinforcement Learning via Score Matchingcited by 5
  24. 2022Augmented RBMLE-UCB Approach for Adaptive Control of Linear Quadratic Systemscited by 5
  25. 2022Rate-Optimal Online Convex Optimization in Adaptive Linear Controlcited by 5
  26. 2022Meta-Learning Online Control for Linear Dynamical Systemscited by 5
  27. 2022Best of Both Worlds in Online Control: Competitive Ratio and Policy Regretcited by 5
  28. 2023Non-asymptotic System Identification for Linear Systems with Nonlinear Policiescited by 5
  29. 2024Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPscited by 5
  30. 2025The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspectivecited by 5
  31. 2021Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systemscited by 4
  32. 2021Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systemscited by 4
  33. 2022Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamicscited by 4
  34. 2023Optimal Sample Selection Through Uncertainty Estimation and Its Application in Deep Learningcited by 4
  35. 2023Sample Efficient Reinforcement Learning with Partial Dynamics Knowledgecited by 4
  36. 2024Regret Analysis of Multi-task Representation Learning for Linear-Quadratic Adaptive Controlcited by 4
  37. 2024Local Linearity: the Key for No-regret Reinforcement Learning in Continuous MDPscited by 4
  38. 2025Finite Sample Identification of Partially Observed Bilinear Dynamical Systemscited by 4

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