mlsanityData to 7 Oct 2026

Input Perturbations for Adaptive Control and Learning

arXiv 1811.04258 ↗First posted 10 Nov 2018eess.SY cs.LG cs.ROcited by 18

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Abstract (arXiv)

This paper studies adaptive algorithms for simultaneous regulation (i.e., control) and estimation (i.e., learning) of Multiple Input Multiple Output (MIMO) linear dynamical systems. It proposes practical, easy to implement control policies based on perturbations of input signals. Such policies are shown to achieve a worst-case regret that scales as the square-root of the time horizon, and holds uniformly over time. Further, it discusses specific settings where such greedy policies attain the information theoretic lower bound of logarithmic regret. To establish the results, recent advances on self-normalized martingales together with a novel method of policy decomposition are leveraged.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Nov 2018.

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Citing papers per year: 2021: 9; 2022: 7; 2023: 2.

18 papers.

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  1. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 52
  2. 2021Joint Learning of Linear Time-Invariant Dynamical Systemscited by 16
  3. 2021Minimal Expected Regret in Linear Quadratic Controlcited by 13
  4. 2022Regret Lower Bounds for Learning Linear Quadratic Gaussian Systemscited by 11
  5. 2022Augmented RBMLE-UCB Approach for Adaptive Control of Linear Quadratic Systemscited by 5
  6. 2021Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systemscited by 4
  7. 2021Strong Consistency and Rate of Convergence of Switched Least Squares System Identification for Autonomous Markov Jump Linear Systemscited by 4
  8. 2022Joint Learning-Based Stabilization of Multiple Unknown Linear Systemscited by 3
  9. 2022Efficient Algorithms for Learning to Control Bandits with Unobserved Contextscited by 3
  10. 2021Scalable regret for learning to control network-coupled subsystems with unknown dynamicscited by 2
  11. 2021Bayesian Algorithms Learn to Stabilize Unknown Continuous-Time Systemscited by 2
  12. 2022Worst-case Performance of Greedy Policies in Bandits with Imperfect Context Observationscited by 2
6 more
  1. 2021A relaxed technical assumption for posterior sampling-based reinforcement learning for control of unknown linear systemscited by 1
  2. 2021Safe Linear-Quadratic Dual Control with Almost Sure Performance Guaranteecited by 0
  3. 2021Reinforcement Learning Policies in Continuous-Time Linear Systemscited by 0
  4. 2022Regret Analysis of Certainty Equivalence Policies in Continuous-Time Linear-Quadratic Systemscited by 0
  5. 2023Almost Surely √T Regret for Adaptive LQRcited by 0
  6. 2023Finite Time Regret Bounds for Minimum Variance Control of Autoregressive Systems with Exogenous Inputscited by 0