mlsanityData to 7 Oct 2026

Logarithmic Regret for Adversarial Online Control

arXiv 2003.00189 ↗First posted 29 Feb 2020cs.LG math.OC stat.MLcited by 41

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Abstract (arXiv)

We introduce a new algorithm for online linear-quadratic control in a known system subject to adversarial disturbances. Existing regret bounds for this setting scale as √T unless strong stochastic assumptions are imposed on the disturbance process. We give the first algorithm with logarithmic regret for arbitrary adversarial disturbance sequences, provided the state and control costs are given by known quadratic functions. Our algorithm and analysis use a characterization for the optimal offline control law to reduce the online control problem to (delayed) online learning with approximate advantage functions. Compared to previous techniques, our approach does not need to control movement costs for the iterates, leading to logarithmic regret.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Feb 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 10; 2023: 8; 2024: 7; 2025: 6; 2026: 4.

41 papers.

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  1. 2021Non-stationary Online Learning with Memory and Non-stochastic Controlcited by 33
  2. 2023Efficient Methods for Non-stationary Online Learningcited by 15
  3. 2021Adversarial Tracking Control via Strongly Adaptive Online Learning with Memorycited by 14
  4. 2021Lazy OCO: Online Convex Optimization on a Switching Budgetcited by 14
  5. 2021Regret-optimal Estimation and Controlcited by 10
  6. 2022Exploiting the Curvature of Feasible Sets for Faster Projection-Free Online Learningcited by 10
  7. 2021Competitive Controlcited by 8
  8. 2023Optimal Rates for Bandit Nonstochastic Controlcited by 7
  9. 2022Optimal Dynamic Regret in LQR Controlcited by 6
  10. 2022Model Predictive Control via On-Policy Imitation Learningcited by 6
  11. 2022Online Convex Optimization with Unbounded Memorycited by 6
  12. 2022Best of Both Worlds in Online Control: Competitive Ratio and Policy Regretcited by 5
29 more
  1. 2023Online Nonstochastic Control with Adversarial and Static Constraintscited by 5
  2. 2024Predictive Linear Online Tracking for Unknown Targetscited by 5
  3. 2022Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamicscited by 4
  4. 2023PAC-Bayesian bounds for learning LTI-ss systems with input from empirical losscited by 3
  5. 2023Adaptive Online Non-stochastic Controlcited by 3
  6. 2024Optimistic Online Non-stochastic Control via FTRLcited by 3
  7. 2022Optimal Competitive-Ratio Controlcited by 2
  8. 2024Length independent generalization bounds for deep SSM architectures via Rademacher contraction and stability constraintscited by 2
  9. 2024Incremental Online Learning of Randomized Neural Network with Forward Regularizationcited by 2
  10. 2025Offline Reinforcement Learning via Inverse Optimizationcited by 2
  11. 2025A New Approach to Controlling Linear Dynamical Systemscited by 2
  12. 2025A Simple, Optimal and Efficient Algorithm for Online Exp-Concave Optimizationcited by 2
  13. 2026Parameter-free Dynamic Regret: Time-varying Movement Costs, Delayed Feedback, and Memorycited by 2
  14. 2022PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Modelscited by 1
  15. 2024Online Residual Learning from Offline Experts for Pedestrian Trackingcited by 1
  16. 2021Regret-Optimal LQR Controlcited by 0
  17. 2022Rate-matching the regret lower-bound in the linear quadratic regulator with unknown dynamicscited by 0
  18. 2022Learning to Control under Time-Varying Environmentcited by 0
  19. 2023Learning to Seek: Multi-Agent Online Source Seeking Against Non-Stochastic Disturbancescited by 0
  20. 2023PAC bounds of continuous Linear Parameter-Varying systems related to neural ODEscited by 0
  21. 2023Data-Driven Adversarial Online Control for Unknown Linear Systemscited by 0
  22. 2024Online Control of Linear Systems under Unbounded Noisecited by 0
  23. 2024A finite-sample generalization bound for stable LPV systemscited by 0
  24. 2025Efficient Spectral Control of Partially Observed Linear Dynamical Systemscited by 0
  25. 2025Online Multi-Agent Control with Adversarial Disturbancescited by 0
  26. 2025Smoothed Online Optimization for Target Tracking: Robust and Learning-Augmented Algorithmscited by 0
  27. 2026Online Nonstochastic Prediction: Logarithmic Regret via Predictive Online Least Squarescited by 0
  28. 2026A Memory Efficient Unified Algorithm for Online Learning of Linear Dynamical Systemscited by 0
  29. 2026Self-Adaptive Learning and Model Predictive Control for Tracking Unknown Dynamics with No Regretcited by 0