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The Power of Predictions in Online Control

arXiv 2006.07569 ↗First posted 13 Jun 2020math.OC cs.SY eess.SYcited by 31

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Abstract (arXiv)

We study the impact of predictions in online Linear Quadratic Regulator control with both stochastic and adversarial disturbances in the dynamics. In both settings, we characterize the optimal policy and derive tight bounds on the minimum cost and dynamic regret. Perhaps surprisingly, our analysis shows that the conventional greedy MPC approach is a near-optimal policy in both stochastic and adversarial settings. Specifically, for length-T problems, MPC requires only O(log T) predictions to reach O(1) dynamic regret, which matches (up to lower-order terms) our lower bound on the required prediction horizon for constant regret.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Jun 2020.

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Citing papers per year: 2021: 5; 2022: 6; 2023: 8; 2024: 6; 2025: 1; 2026: 5.

31 papers.

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  1. 2021Meta-Adaptive Nonlinear Control: Theory and Algorithmscited by 23
  2. 2023Optimal Exploration for Model-Based RL in Nonlinear Systemscited by 17
  3. 2021Adversarial Tracking Control via Strongly Adaptive Online Learning with Memorycited by 14
  4. 2023DATT: Deep Adaptive Trajectory Tracking for Quadrotor Controlcited by 11
  5. 2024Reinforcement Learning with Lookahead Informationcited by 8
  6. 2023Deep Model Predictive Optimizationcited by 7
  7. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  8. 2022Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environmentscited by 6
  9. 2021Online Optimization with Feedback Delay and Nonlinear Switching Costcited by 5
  10. 2024Predictive Linear Online Tracking for Unknown Targetscited by 5
  11. 2021Online Learning for Predictive Control with Provable Regret Guaranteescited by 3
  12. 2022Implications of Regret on Stability of Linear Dynamical Systemscited by 3
19 more
  1. 2023Adaptive Online Non-stochastic Controlcited by 3
  2. 2024CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Designcited by 3
  3. 2024Optimistic Online Non-stochastic Control via FTRLcited by 3
  4. 2025Reinforcement Learning with Imperfect Transition Predictions: A Bellman-Jensen Approachcited by 3
  5. 2026AdaReP:Adaptive Re-Planning under Model Mismatch for Neural World-Model Predictive Controlcited by 3
  6. 2022Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objectscited by 2
  7. 2024Predictive Control and Regret Analysis of Non-Stationary MDP with Look-ahead Informationcited by 2
  8. 2022Interstellar Object Accessibility and Mission Designcited by 1
  9. 2022A Critical Review of Traffic Signal Control and A Novel Unified View of Reinforcement Learning and Model Predictive Control Approaches for Adaptive Traffic Signal Controlcited by 1
  10. 2023Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based controlcited by 1
  11. 2023Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbancescited by 1
  12. 2024Preparing for Black Swans: The Antifragility Imperative for Machine Learningcited by 1
  13. 2022Bayesian Learning Approach to Model Predictive Controlcited by 0
  14. 2023Sub-linear Regret in Adaptive Model Predictive Controlcited by 0
  15. 2023Data-Guided Regulator for Adaptive Nonlinear Controlcited by 0
  16. 2026Reinforcement Learning with Multi-Step Lookahead Information Via Adaptive Batchingcited by 0
  17. 2026Constrained Online Convex Optimization with Memory and Predictionscited by 0
  18. 2026Learning to Spend: Model Predictive Control for Budgeting under Non-Stationary Returnscited by 0
  19. 2026A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systemscited by 0