mlsanityData to 7 Oct 2026

Logarithmic Regret for Online Control

arXiv 1909.05062 ↗First posted 11 Sep 2019cs.LG math.OC stat.MLcited by 38

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Abstract (arXiv)

We study optimal regret bounds for control in linear dynamical systems under adversarially changing strongly convex cost functions, given the knowledge of transition dynamics. This includes several well studied and fundamental frameworks such as the Kalman filter and the linear quadratic regulator. State of the art methods achieve regret which scales as O(√T), where T is the time horizon. We show that the optimal regret in this setting can be significantly smaller, scaling as O(poly(log T)). This regret bound is achieved by two different efficient iterative methods, online gradient descent and online natural gradient.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Sep 2019.

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Citing papers per year: 2021: 10; 2022: 7; 2023: 5; 2024: 9; 2025: 3; 2026: 4.

38 papers.

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  1. 2021Adversarial Tracking Control via Strongly Adaptive Online Learning with Memorycited by 14
  2. 2021Lazy OCO: Online Convex Optimization on a Switching Budgetcited by 14
  3. 2023Sample-Efficient Linear Representation Learning from Non-IID Non-Isotropic Datacited by 12
  4. 2021Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regretcited by 10
  5. 2021Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guaranteescited by 10
  6. 2022Exploiting the Curvature of Feasible Sets for Faster Projection-Free Online Learningcited by 10
  7. 2021A Regret Minimization Approach to Iterative Learning Controlcited by 8
  8. 2023Optimal Rates for Bandit Nonstochastic Controlcited by 7
  9. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  10. 2022Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environmentscited by 6
  11. 2022Online Convex Optimization with Unbounded Memorycited by 6
  12. 2025Universal Sequence Preconditioningcited by 6
26 more
  1. 2021Online Optimization with Feedback Delay and Nonlinear Switching Costcited by 5
  2. 2022Rate-Optimal Online Convex Optimization in Adaptive Linear Controlcited by 5
  3. 2023Online Nonstochastic Control with Adversarial and Static Constraintscited by 5
  4. 2024Predictive Linear Online Tracking for Unknown Targetscited by 5
  5. 2021Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systemscited by 4
  6. 2022Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamicscited by 4
  7. 2021Online Learning for Predictive Control with Provable Regret Guaranteescited by 3
  8. 2022Implications of Regret on Stability of Linear Dynamical Systemscited by 3
  9. 2022Dynamical Linear Banditscited by 3
  10. 2023Adaptive Online Non-stochastic Controlcited by 3
  11. 2024Optimistic Online Non-stochastic Control via FTRLcited by 3
  12. 2024Online Control in Population Dynamicscited by 2
  13. 2024Combining Federated Learning and Control: A Surveycited by 2
  14. 2024Predictive Control and Regret Analysis of Non-Stationary MDP with Look-ahead Informationcited by 2
  15. 2024Tight Rates for Bandit Control Beyond Quadraticscited by 2
  16. 2025A New Approach to Controlling Linear Dynamical Systemscited by 2
  17. 2026Parameter-free Dynamic Regret: Time-varying Movement Costs, Delayed Feedback, and Memorycited by 2
  18. 2023Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbancescited by 1
  19. 2024Online Stackelberg Optimization via Nonlinear Controlcited by 1
  20. 2021Regret-Optimal LQR Controlcited by 0
  21. 2024Online Control of Linear Systems under Unbounded Noisecited by 0
  22. 2024Regret Analysis of Policy Optimization over Submanifolds for Linearly Constrained Online LQGcited by 0
  23. 2025Efficient Spectral Control of Partially Observed Linear Dynamical Systemscited by 0
  24. 2026Online Nonstochastic Prediction: Logarithmic Regret via Predictive Online Least Squarescited by 0
  25. 2026A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systemscited by 0
  26. 2026Block Optimism for Nonstationary Bandits with Latent Linear Dynamicscited by 0