# Online Learning for Predictive Control with Provable Regret Guarantees

arXiv: https://arxiv.org/abs/2111.15041 · HTML: https://mlsanity.com/paper/2111.15041/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 30 Nov 2021.

## Builds on (most cited first, 15 of 15)

- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Learning Linear-Quadratic Regulators Efficiently with only √T Regret](https://mlsanity.com/paper/1902.06223/) (2019)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [The Nonstochastic Control Problem](https://mlsanity.com/paper/1911.12178/) (2019)
- [Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis](https://mlsanity.com/paper/1906.11378/) (2019)
- [Logarithmic Regret for Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [Smoothed Online Optimization for Regression and Control](https://mlsanity.com/paper/1810.10132/) (2018)
- [Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems](https://mlsanity.com/paper/2106.10497/) (2021)
- [Adaptive MPC under Time Varying Uncertainty: Robust and Stochastic](https://mlsanity.com/paper/1909.13473/) (2019)
- [Robust Optimal Control with Adjustable Uncertainty Sets](https://mlsanity.com/paper/1511.04700/) (2015)

## Built on by (most cited first, 3 of 3)

- [AdaReP:Adaptive Re-Planning under Model Mismatch for Neural World-Model Predictive Control](https://mlsanity.com/paper/2606.23079/) (2026)
- [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)
- [SCaLE: Switching Cost aware Learning and Exploration](https://mlsanity.com/paper/2601.09042/) (2026)

## Abstract (arXiv)

We study the problem of online learning in predictive control of an unknown linear dynamical system with time varying cost functions which are unknown apriori. Specifically, we study the online learning problem where the control algorithm does not know the true system model and has only access to a fixed-length (that does not grow with the control horizon) preview of the future cost functions. The goal of the online algorithm is to minimize the dynamic regret, defined as the difference between the cumulative cost incurred by the algorithm and that of the best sequence of actions in hindsight. We propose two different online Model Predictive Control (MPC) algorithms to address this problem, namely Certainty Equivalence MPC (CE-MPC) algorithm and Optimistic MPC (O-MPC) algorithm. We show that under the standard stability assumption for the model estimate, the CE-MPC algorithm achieves O(T2/3) dynamic regret. We then extend this result to the setting where the stability assumption holds only for the true system model by proposing the O-MPC algorithm. We show that the O-MPC algorithm also achieves O(T2/3) dynamic regret, at the cost of some additional computation. We also present numerical studies to demonstrate the performance of our algorithm.