# On the Regret Analysis of Online LQR Control with Predictions

arXiv: https://arxiv.org/abs/2102.01309 · HTML: https://mlsanity.com/paper/2102.01309/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2021.

## Built on by (most cited first, 22 of 22)

- [Provable Sim-to-real Transfer in Continuous Domain with Partial Observations](https://mlsanity.com/paper/2210.15598/) (2022)
- [Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictions](https://mlsanity.com/paper/2307.10524/) (2023)
- [Regret Analysis of Distributed Online LQR Control for Unknown LTI Systems](https://mlsanity.com/paper/2105.07310/) (2021)
- [Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2309.14648/) (2023)
- [The Value of Reward Lookahead in Reinforcement Learning](https://mlsanity.com/paper/2403.11637/) (2024)
- [Predictive Linear Online Tracking for Unknown Targets](https://mlsanity.com/paper/2402.10036/) (2024)
- [On the Hardness of Reinforcement Learning with Transition Look-Ahead](https://mlsanity.com/paper/2510.19372/) (2025)
- [Implications of Regret on Stability of Linear Dynamical Systems](https://mlsanity.com/paper/2211.07411/) (2022)
- [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)
- [Exact Recovery for System Identification with More Corrupt Data than Clean Data](https://mlsanity.com/paper/2305.10506/) (2023)
- [OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression](https://mlsanity.com/paper/2105.13271/) (2021)
- [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)
- [Anytime-Competitive Reinforcement Learning with Policy Prior](https://mlsanity.com/paper/2311.01568/) (2023)
- [Out-of-Distribution-Aware Electric Vehicle Charging](https://mlsanity.com/paper/2311.05941/) (2023)
- [Regret Analysis of Online LQR Control via Trajectory Prediction and Tracking: Extended Version](https://mlsanity.com/paper/2302.10411/) (2023)
- [Sub-linear Regret in Adaptive Model Predictive Control](https://mlsanity.com/paper/2310.04842/) (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)
- [A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systems](https://mlsanity.com/paper/2608.02375/) (2026)

## 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.