mlsanityData to 7 Oct 2026

Statistical Learning Theory for Control: A Finite Sample Perspective

arXiv 2209.05423 ↗First posted 12 Sep 2022eess.SY cs.LG cs.SYcited by 52

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Abstract (arXiv)

This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been substantial progress across all areas of control, the theory is most well-developed when it comes to linear system identification and learning for the linear quadratic regulator, which are the focus of this manuscript. From a theoretical perspective, much of the labor underlying these advances has been in adapting tools from modern high-dimensional statistics and learning theory. While highly relevant to control theorists interested in integrating tools from machine learning, the foundational material has not always been easily accessible. To remedy this, we provide a self-contained presentation of the relevant material, outlining all the key ideas and the technical machinery that underpin recent results. We also present a number of open problems and future directions.

Key facts. Cited by 52 papers in the map (data through 7 Oct 2026). Builds on 62 of its 135 references that are in the map. First posted on arXiv 12 Sep 2022.

Builds on

62 of 135 references.

References · 62

  1. 2015Continuous control with deep reinforcement learningcited by 3,279
  2. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 526
  3. 2018Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulatorcited by 211
  4. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  5. 2017On the Sample Complexity of the Linear Quadratic Regulatorcited by 151
  6. 2020Naive Exploration is Optimal for Online LQRcited by 111
  7. 2015Low-rank Solutions of Linear Matrix Equations via Procrustes Flowcited by 97
  8. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  9. 2018Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulatorcited by 86
  10. 2020Improper Learning for Non-Stochastic Controlcited by 83
  11. 2016Gradient Descent Learns Linear Dynamical Systemscited by 78
  12. 2020Active Learning for Nonlinear System Identification with Guaranteescited by 78
38 more
  1. 2019Learning Linear-Quadratic Regulators Efficiently with only √T Regretcited by 67
  2. 2019Finite Sample Analysis of Stochastic System Identificationcited by 67
  3. 2017Finite Time Identification in Unstable Linear Systemscited by 66
  4. 2019Learning Linear Dynamical Systems with Semi-Parametric Least Squarescited by 58
  5. 2020Least Squares Regression with Markovian Data: Fundamental Limits and Algorithmscited by 56
  6. 2014Learning without Concentrationcited by 50
  7. 2020Logarithmic Regret Bound in Partially Observable Linear Dynamical Systemscited by 46
  8. 2020Learning nonlinear dynamical systems from a single trajectorycited by 46
  9. 2020Policy Gradient Methods for the Noisy Linear Quadratic Regulator over a Finite Horizoncited by 43
  10. 2021Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overviewcited by 42
  11. 2020Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systemscited by 39
  12. 2020Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectoriescited by 38
  13. 2021On the Sample Complexity of Stability Constrained Imitation Learningcited by 38
  14. 2018The Gap Between Model-Based and Model-Free Methods on the Linear Quadratic Regulator: An Asymptotic Viewpointcited by 36
  15. 2019Exact minimax risk for linear least squares, and the lower tail of sample covariance matricescited by 34
  16. 2020Active Learning for Identification of Linear Dynamical Systemscited by 33
  17. 2020Logarithmic Regret for Learning Linear Quadratic Regulators Efficientlycited by 33
  18. 2022Learning with little mixingcited by 33
  19. 2018Safely Learning to Control the Constrained Linear Quadratic Regulatorcited by 31
  20. 2020Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimatorcited by 26
  21. 2022Single Trajectory Nonparametric Learning of Nonlinear Dynamicscited by 26
  22. 2021Stabilizing Dynamical Systems via Policy Gradient Methodscited by 24
  23. 2022Learning from many trajectoriescited by 24
  24. 2020Online Learning of the Kalman Filter with Logarithmic Regretcited by 21
  25. 2022TaSIL: Taylor Series Imitation Learningcited by 21
  26. 2019Sample Complexity Lower Bounds for Linear System Identificationcited by 20
  27. 2019Learning Sparse Dynamical Systems from a Single Sample Trajectorycited by 20
  28. 2021Linear Systems can be Hard to Learncited by 20
  29. 2019A Tutorial on Concentration Bounds for System Identificationcited by 19
  30. 2018Input Perturbations for Adaptive Control and Learningcited by 18
  31. 2020No-Regret Prediction in Marginally Stable Systemscited by 18
  32. 2020Efficient Optimistic Exploration in Linear-Quadratic Regulators via Lagrangian Relaxationcited by 18
  33. 2021Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systemscited by 17
  34. 2017Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identificationcited by 16
  35. 2018On-Line Learning of Linear Dynamical Systems: Exponential Forgetting in Kalman Filterscited by 16
  36. 2021Task-Optimal Exploration in Linear Dynamical Systemscited by 15
  37. 2014Learning without Concentration for General Loss Functionscited by 13
  38. 2021Minimal Expected Regret in Linear Quadratic Controlcited by 13

50 most cited of 62 All 62 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 16; 2024: 18; 2025: 9; 2026: 6.

52 papers.

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  1. 2023Transformers as Algorithms: Generalization and Stability in In-context Learningcited by 220
  2. 2024From Self-Attention to Markov Models: Unveiling the Dynamics of Generative Transformerscited by 34
  3. 2023A Tutorial on the Non-Asymptotic Theory of System Identificationcited by 26
  4. 2023A New Approach to Learning Linear Dynamical Systemscited by 23
  5. 2022FedSysID: A Federated Approach to Sample-Efficient System Identificationcited by 15
  6. 2024Sharp Rates in Dependent Learning Theory: Avoiding Sample Size Deflation for the Square Losscited by 10
  7. 2023Smoothed Online Learning for Prediction in Piecewise Affine Systemscited by 9
  8. 2024Active Learning for Control-Oriented Identification of Nonlinear Systemscited by 7
  9. 2022Towards a Theoretical Foundation of Policy Optimization for Learning Control Policiescited by 6
  10. 2023The noise level in linear regression with dependent datacited by 6
  11. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  12. 2023Nonasymptotic Regret Analysis of Adaptive Linear Quadratic Control with Model Misspecificationcited by 6
38 more
  1. 2023Oracle-Efficient Smoothed Online Learning for Piecewise Continuous Decision Makingcited by 5
  2. 2025The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspectivecited by 5
  3. 2025Heavy-Tailed Linear Bandits: Huber Regression with One-Pass Updatecited by 5
  4. 2023Controlgym: Large-Scale Control Environments for Benchmarking Reinforcement Learning Algorithmscited by 4
  5. 2024High-dimensional analysis of ridge regression for non-identically distributed data with a variance profilecited by 4
  6. 2024Outlier-Robust Linear System Identification Under Heavy-tailed Noisecited by 4
  7. 2024Sample Complexity Bounds for Linear System Identification from a Finite Setcited by 3
  8. 2024Long-Context Linear System Identificationcited by 3
  9. 2023Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraintscited by 2
  10. 2023Exact Recovery for System Identification with More Corrupt Data than Clean Datacited by 2
  11. 2022A note on the smallest eigenvalue of the empirical covariance of causal Gaussian processescited by 1
  12. 2023Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based controlcited by 1
  13. 2023Learning and Concentration for High Dimensional Linear Gaussians: an Invariant Subspace Approachcited by 1
  14. 2023From Spectral Theorem to Statistical Independence with Application to System Identificationcited by 1
  15. 2023Regret Analysis of Learning-Based Linear Quadratic Gaussian Control with Additive Explorationcited by 1
  16. 2024Model-Free Learning for the Linear Quadratic Regulator over Rate-Limited Channelscited by 1
  17. 2024Finite Sample Frequency Domain Identificationcited by 1
  18. 2024Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Methodcited by 1
  19. 2024Single Trajectory Conformal Predictioncited by 1
  20. 2024Exact Recovery Guarantees for Parameterized Nonlinear System Identification Problem under Sparse Disturbances or Semi-Oblivious Attackscited by 1
  21. 2024End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic datacited by 1
  22. 2025A finite-sample bound for identifying partially observed linear switched systems from a single trajectorycited by 1
  23. 2025High Effort, Low Gain: Fundamental Limits of Active Learning for Linear Dynamical Systemscited by 1
  24. 2025Concentration inequalities for semidefinite least squares based on datacited by 1
  25. 2025Finite-sample guarantees for data-driven forward-backward operator methodscited by 1
  26. 2023Estimation Sample Complexity of a Class of Nonlinear Continuous-time Systemscited by 0
  27. 2024A finite-sample generalization bound for stable LPV systemscited by 0
  28. 2024On the stability of gradient descent with second order dynamics for time-varying cost functionscited by 0
  29. 2024Causal Learning in Biomedical Applications: Krebs Cycle as a Benchmarkcited by 0
  30. 2024Finite Sample Analysis of Distribution-Free Confidence Ellipsoids for Linear Regressioncited by 0
  31. 2024Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systemscited by 0
  32. 2025Subgradient Method for System Identification with Non-Smooth Objectivescited by 0
  33. 2025Boosting-Enabled Robust System Identification of Partially Observed LTI Systems Under Heavy-Tailed Noisecited by 0
  34. 2025Frequency Response Identification of Low-Order Systems: Finite-Sample Analysiscited by 0
  35. 2026Uniform error bounds for quantized dynamical modelscited by 0
  36. 2026Reinforcement Learning for Control with Probabilistic Stability Guarantee: A Finite-Sample Approachcited by 0
  37. 2026Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part IIcited by 0
  38. 2026Optimizing Digital Therapeutic Interventions: Online Learning under Endogenous Adherencecited by 0

50 most cited of 52 All 52 (JSON)