mlsanityData to 7 Oct 2026

Rate-Optimal Online Convex Optimization in Adaptive Linear Control

arXiv 2206.01426 ↗First posted 3 Jun 2022cs.LG math.OC stat.MLcited by 5

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Abstract (arXiv)

We consider the problem of controlling an unknown linear dynamical system under adversarially changing convex costs and full feedback of both the state and cost function. We present the first computationally-efficient algorithm that attains an optimal smash√T-regret rate compared to the best stabilizing linear controller in hindsight, while avoiding stringent assumptions on the costs such as strong convexity. Our approach is based on a careful design of non-convex lower confidence bounds for the online costs, and uses a novel technique for computationally-efficient regret minimization of these bounds that leverages their particular non-convex structure.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 22 of its 45 references that are in the map. First posted on arXiv 3 Jun 2022.

Builds on

22 of 45 references.

References · 22

  1. 2018Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulatorcited by 211
  2. 2020Naive Exploration is Optimal for Online LQRcited by 111
  3. 2019Online Control with Adversarial Disturbancescited by 92
  4. 2018Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulatorcited by 86
  5. 2020Improper Learning for Non-Stochastic Controlcited by 83
  6. 2019Learning Linear-Quadratic Regulators Efficiently with only √T Regretcited by 67
  7. 2018Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systemscited by 56
  8. 2018Online Linear Quadratic Controlcited by 55
  9. 2020Near-optimal Regret Bounds for Stochastic Shortest Pathcited by 50
  10. 2020Logarithmic Regret Bound in Partially Observable Linear Dynamical Systemscited by 46
  11. 2020Black-Box Control for Linear Dynamical Systemscited by 43
  12. 2019Logarithmic Regret for Online Controlcited by 38
10 more
  1. 2018The Gap Between Model-Based and Model-Free Methods on the Linear Quadratic Regulator: An Asymptotic Viewpointcited by 36
  2. 2020Logarithmic Regret for Learning Linear Quadratic Regulators Efficientlycited by 33
  3. 2018Online learning over a finite action set with limited switchingcited by 21
  4. 2020Non-Stochastic Control with Bandit Feedbackcited by 17
  5. 2013Efficient Reinforcement Learning for High Dimensional Linear Quadratic Systemscited by 13
  6. 2018Model-Free Linear Quadratic Control via Reduction to Expert Predictioncited by 10
  7. 2020Bandit Linear Controlcited by 10
  8. 2021Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regretcited by 10
  9. 2020Geometric Exploration for Online Controlcited by 9
  10. 2022Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamicscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 1; 2026: 1.

5 papers.

  1. 2023Online Nonstochastic Model-Free Reinforcement Learningcited by 2
  2. 2023Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbancescited by 1
  3. 2024Optimistic Safety for Online Convex Optimization with Unknown Linear Constraintscited by 1
  4. 2025The Safety-Privacy Tradeoff in Linear Banditscited by 0
  5. 2026ASTRA: ADMM-Accelerated Topology Reconfiguration for Dynamic Satellite Constellationscited by 0