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The Nonstochastic Control Problem

arXiv 1911.12178 ↗First posted 27 Nov 2019cs.LG stat.MLcited by 52

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Abstract (arXiv)

We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions. In contrast to classical control, the a priori determination of an optimal controller here is hindered by the latter's dependence on the yet unknown perturbations and costs. Instead, we measure regret against an optimal linear policy in hindsight, and give the first efficient algorithm that guarantees a sublinear regret bound, scaling as T^{2/3}, in this setting.

Key facts. Cited by 52 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Nov 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 17; 2022: 8; 2023: 9; 2024: 8; 2025: 8; 2026: 2.

52 papers.

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  1. 2024Online DPO: Online Direct Preference Optimization with Fast-Slow Chasingcited by 38
  2. 2021Non-stationary Online Learning with Memory and Non-stochastic Controlcited by 33
  3. 2021Stabilizing Dynamical Systems via Policy Gradient Methodscited by 24
  4. 2021Streaming Linear System Identification with Reverse Experience Replaycited by 17
  5. 2023Efficient Methods for Non-stationary Online Learningcited by 15
  6. 2025Generative Models in Decision Making: A Surveycited by 14
  7. 2021Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear Systemcited by 13
  8. 2022Online Control of Unknown Time-Varying Dynamical Systemscited by 13
  9. 2021Deluca -- A Differentiable Control Library: Environments, Methods, and Benchmarkingcited by 10
  10. 2021Regret-optimal Estimation and Controlcited by 10
  11. 2021Learning from Censored and Dependent Data: The case of Linear Dynamicscited by 9
  12. 2021A Regret Minimization Approach to Iterative Learning Controlcited by 8
38 more
  1. 2021Competitive Controlcited by 8
  2. 2023Optimal Rates for Bandit Nonstochastic Controlcited by 7
  3. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  4. 2022Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environmentscited by 6
  5. 2022Optimal Dynamic Regret in LQR Controlcited by 6
  6. 2022Online Convex Optimization with Unbounded Memorycited by 6
  7. 2023Nonasymptotic Regret Analysis of Adaptive Linear Quadratic Control with Model Misspecificationcited by 6
  8. 2022Meta-Learning Online Control for Linear Dynamical Systemscited by 5
  9. 2022Best of Both Worlds in Online Control: Competitive Ratio and Policy Regretcited by 5
  10. 2023Efficient Online Learning with Memory via Frank-Wolfe Optimization: Algorithms with Bounded Dynamic Regret and Applications to Controlcited by 5
  11. 2025The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspectivecited by 5
  12. 2025Universal Learning of Nonlinear Dynamicscited by 5
  13. 2021Robust Online Control with Model Misspecificationcited by 4
  14. 2021Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systemscited by 4
  15. 2024Regret Analysis of Multi-task Representation Learning for Linear-Quadratic Adaptive Controlcited by 4
  16. 2021DiffLoop: Tuning PID controllers by differentiating through the feedback loopcited by 3
  17. 2021Online Learning for Predictive Control with Provable Regret Guaranteescited by 3
  18. 2023Adaptive Online Non-stochastic Controlcited by 3
  19. 2024Optimistic Online Non-stochastic Control via FTRLcited by 3
  20. 2024Provable Length Generalization in Sequence Prediction via Spectral Filteringcited by 3
  21. 2022Online Convex Optimization with Long Term Constraints for Predictable Sequencescited by 2
  22. 2023Online Nonstochastic Model-Free Reinforcement Learningcited by 2
  23. 2024Online Control in Population Dynamicscited by 2
  24. 2024Combining Federated Learning and Control: A Surveycited by 2
  25. 2025Offline Reinforcement Learning via Inverse Optimizationcited by 2
  26. 2022Regret Analysis of Online Gradient Descent-based Iterative Learning Control with Model Mismatchcited by 1
  27. 2023Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbancescited by 1
  28. 2021Regret-Optimal Filtering for Prediction and Estimationcited by 0
  29. 2021Regret-Optimal LQR Controlcited by 0
  30. 2021WAX-ML: A Python library for machine learning and feedback loops on streaming datacited by 0
  31. 2023Learning to Seek: Multi-Agent Online Source Seeking Against Non-Stochastic Disturbancescited by 0
  32. 2023Data-Driven Adversarial Online Control for Unknown Linear Systemscited by 0
  33. 2024Online Control of Linear Systems under Unbounded Noisecited by 0
  34. 2024Regret Analysis of Policy Optimization over Submanifolds for Linearly Constrained Online LQGcited by 0
  35. 2025Regret Analysis: a control perspectivecited by 0
  36. 2025Constrained Online Decision-Making: A Unified Frameworkcited by 0
  37. 2025Online Multi-Agent Control with Adversarial Disturbancescited by 0
  38. 2025Adversarially Robust Multitask Adaptive Controlcited by 0

50 most cited of 52 All 52 (JSON)