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On the Regret Analysis of Online LQR Control with Predictions

arXiv 2102.01309 ↗First posted 2 Feb 2021math.OCcited by 22

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Abstract (arXiv)

In this paper, we study the dynamic regret of online linear quadratic regulator (LQR) control with time-varying cost functions and disturbances. We consider the case where a finite look-ahead window of cost functions and disturbances is available at each stage. The online control algorithm studied in this paper falls into the category of model predictive control (MPC) with a particular choice of terminal costs to ensure the exponential stability of MPC. It is proved that the regret of such an online algorithm decays exponentially fast with the length of predictions. The impact of inaccurate prediction on disturbances is also investigated in this paper.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Feb 2021.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 9; 2024: 3; 2025: 2; 2026: 4.

22 papers.

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  1. 2022Provable Sim-to-real Transfer in Continuous Domain with Partial Observationscited by 9
  2. 2023Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictionscited by 8
  3. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  4. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  5. 2024The Value of Reward Lookahead in Reinforcement Learningcited by 6
  6. 2024Predictive Linear Online Tracking for Unknown Targetscited by 5
  7. 2025On the Hardness of Reinforcement Learning with Transition Look-Aheadcited by 4
  8. 2022Implications of Regret on Stability of Linear Dynamical Systemscited by 3
  9. 2024Optimistic Online Non-stochastic Control via FTRLcited by 3
  10. 2025Reinforcement Learning with Imperfect Transition Predictions: A Bellman-Jensen Approachcited by 3
  11. 2026AdaReP:Adaptive Re-Planning under Model Mismatch for Neural World-Model Predictive Controlcited by 3
  12. 2023Exact Recovery for System Identification with More Corrupt Data than Clean Datacited by 2
10 more
  1. 2021OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regressioncited by 1
  2. 2023Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based controlcited by 1
  3. 2023Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbancescited by 1
  4. 2023Anytime-Competitive Reinforcement Learning with Policy Priorcited by 1
  5. 2023Out-of-Distribution-Aware Electric Vehicle Chargingcited by 1
  6. 2023Regret Analysis of Online LQR Control via Trajectory Prediction and Tracking: Extended Versioncited by 0
  7. 2023Sub-linear Regret in Adaptive Model Predictive Controlcited by 0
  8. 2026Reinforcement Learning with Multi-Step Lookahead Information Via Adaptive Batchingcited by 0
  9. 2026Constrained Online Convex Optimization with Memory and Predictionscited by 0
  10. 2026A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systemscited by 0