# The Power of Predictions in Online Control

arXiv: https://arxiv.org/abs/2006.07569 · HTML: https://mlsanity.com/paper/2006.07569/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2020.

## Built on by (most cited first, 30 of 31)

- [Meta-Adaptive Nonlinear Control: Theory and Algorithms](https://mlsanity.com/paper/2106.06098/) (2021)
- [Optimal Exploration for Model-Based RL in Nonlinear Systems](https://mlsanity.com/paper/2306.09210/) (2023)
- [DATT: Deep Adaptive Trajectory Tracking for Quadrotor Control](https://mlsanity.com/paper/2310.09053/) (2023)
- [Adversarial Tracking Control via Strongly Adaptive Online Learning with Memory](https://mlsanity.com/paper/2102.01623/) (2021)
- [Reinforcement Learning with Lookahead Information](https://mlsanity.com/paper/2406.02258/) (2024)
- [Deep Model Predictive Optimization](https://mlsanity.com/paper/2310.04590/) (2023)
- [Regret Analysis of Distributed Online LQR Control for Unknown LTI Systems](https://mlsanity.com/paper/2105.07310/) (2021)
- [Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environments](https://mlsanity.com/paper/2205.00446/) (2022)
- [Online Optimization with Feedback Delay and Nonlinear Switching Cost](https://mlsanity.com/paper/2111.00095/) (2021)
- [Predictive Linear Online Tracking for Unknown Targets](https://mlsanity.com/paper/2402.10036/) (2024)
- [CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Design](https://mlsanity.com/paper/2401.07369/) (2024)
- [Online Learning for Predictive Control with Provable Regret Guarantees](https://mlsanity.com/paper/2111.15041/) (2021)
- [Implications of Regret on Stability of Linear Dynamical Systems](https://mlsanity.com/paper/2211.07411/) (2022)
- [Adaptive Online Non-stochastic Control](https://mlsanity.com/paper/2310.02261/) (2023)
- [Optimistic Online Non-stochastic Control via FTRL](https://mlsanity.com/paper/2404.03309/) (2024)
- [Reinforcement Learning with Imperfect Transition Predictions: A Bellman-Jensen Approach](https://mlsanity.com/paper/2510.18687/) (2025)
- [AdaReP:Adaptive Re-Planning under Model Mismatch for Neural World-Model Predictive Control](https://mlsanity.com/paper/2606.23079/) (2026)
- [Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objects](https://mlsanity.com/paper/2208.04883/) (2022)
- [A Critical Review of Traffic Signal Control and A Novel Unified View of Reinforcement Learning and Model Predictive Control Approaches for Adaptive Traffic Signal Control](https://mlsanity.com/paper/2211.14426/) (2022)
- [Predictive Control and Regret Analysis of Non-Stationary MDP with Look-ahead Information](https://mlsanity.com/paper/2409.08434/) (2024)
- [Bayesian Learning Approach to Model Predictive Control](https://mlsanity.com/paper/2203.02720/) (2022)
- [Interstellar Object Accessibility and Mission Design](https://mlsanity.com/paper/2210.14980/) (2022)
- [Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control](https://mlsanity.com/paper/2301.07876/) (2023)
- [Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbances](https://mlsanity.com/paper/2310.03206/) (2023)
- [Preparing for Black Swans: The Antifragility Imperative for Machine Learning](https://mlsanity.com/paper/2405.11397/) (2024)
- [Sub-linear Regret in Adaptive Model Predictive Control](https://mlsanity.com/paper/2310.04842/) (2023)
- [Data-Guided Regulator for Adaptive Nonlinear Control](https://mlsanity.com/paper/2311.12230/) (2023)
- [Reinforcement Learning with Multi-Step Lookahead Information Via Adaptive Batching](https://mlsanity.com/paper/2601.10418/) (2026)
- [Constrained Online Convex Optimization with Memory and Predictions](https://mlsanity.com/paper/2603.21375/) (2026)
- [Learning to Spend: Model Predictive Control for Budgeting under Non-Stationary Returns](https://mlsanity.com/paper/2604.27186/) (2026)

## 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.