mlsanityData to 7 Oct 2026

Safely Learning to Control the Constrained Linear Quadratic Regulator

arXiv 1809.10121 ↗First posted 26 Sep 2018math.OC cs.LG stat.MLcited by 31

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Abstract (arXiv)

We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of state and input constraints. This framework involves a novel method for synthesizing robust constraint-satisfying feedback controllers, leveraging newly developed tools from system level synthesis. We connect statistical results with cost sub-optimality bounds to give non-asymptotic guarantees on both estimation and controller performance.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Sep 2018.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 10; 2022: 8; 2023: 8; 2024: 3; 2025: 0; 2026: 1.

31 papers.

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  1. 2021Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learningcited by 337
  2. 2022Saute RL: Almost Surely Safe Reinforcement Learning Using State Augmentationcited by 63
  3. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 52
  4. 2021Reinforcement Learning for Selective Key Applications in Power Systems: Recent Advances and Future Challengescited by 40
  5. 2019On the Global Convergence of Imitation Learning: A Case for Linear Quadratic Regulatorcited by 20
  6. 2021Task-Optimal Exploration in Linear Dynamical Systemscited by 15
  7. 2021Safe Autonomous Racing via Approximate Reachability on Ego-visioncited by 13
  8. 2021Scalable Learning of Safety Guarantees for Autonomous Systems using Hamilton-Jacobi Reachabilitycited by 10
  9. 2021Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guaranteescited by 10
  10. 2023Learning Dynamical Systems by Leveraging Data from Similar Systemscited by 8
  11. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  12. 2022Effects of Safety State Augmentation on Safe Explorationcited by 5
19 more
  1. 2022Safe Reinforcement Learning via Confidence-Based Filterscited by 5
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  4. 2021Stability-Constrained Markov Decision Processes Using MPCcited by 4
  5. 2021DESTA: A Framework for Safe Reinforcement Learning with Markov Games of Interventioncited by 4
  6. 2022Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraintscited by 3
  7. 2024Combining Federated Learning and Control: A Surveycited by 2
  8. 2022Adaptive Robust Model Predictive Control via Uncertainty Cancellationcited by 1
  9. 2023Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based controlcited by 1
  10. 2024Exact Recovery Guarantees for Parameterized Nonlinear System Identification Problem under Sparse Disturbances or Semi-Oblivious Attackscited by 1
  11. 2021Differentiable Robust LQR Layerscited by 0
  12. 2021Learning Safety Filters for Unknown Discrete-Time Linear Systemscited by 0
  13. 2022System Identification via Nuclear Norm Regularizationcited by 0
  14. 2022Learning Nonlinear Couplings in Network of Agents from a Single Sample Trajectorycited by 0
  15. 2023Safely Learning Dynamical Systemscited by 0
  16. 2023Finite Time Regret Bounds for Minimum Variance Control of Autoregressive Systems with Exogenous Inputscited by 0
  17. 2023Learning to Stabilize Online Reinforcement Learning in Unbounded State Spacescited by 0
  18. 2024Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problemcited by 0
  19. 2026When Can Safe Controllers Adapt? Information before Commitmentcited by 0