# Data-Driven Adversarial Online Control for Unknown Linear Systems

arXiv: https://arxiv.org/abs/2308.08138 · HTML: https://mlsanity.com/paper/2308.08138/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 16 Aug 2023.

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

- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [The Nonstochastic Control Problem](https://mlsanity.com/paper/1911.12178/) (2019)
- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Black-Box Control for Linear Dynamical Systems](https://mlsanity.com/paper/2007.06650/) (2020)
- [Logarithmic Regret for Adversarial Online Control](https://mlsanity.com/paper/2003.00189/) (2020)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Data-Driven Model Predictive Control with Stability and Robustness Guarantees](https://mlsanity.com/paper/1906.04679/) (2019)
- [Introduction to Online Control](https://mlsanity.com/paper/2211.09619/) (2022)
- [A trajectory-based framework for data-driven system analysis and control](https://mlsanity.com/paper/1903.10723/) (2019)
- [Online switching control with stability and regret guarantees](https://mlsanity.com/paper/2301.08445/) (2023)
- [Low-complexity Learning of Linear Quadratic Regulators from Noisy Data](https://mlsanity.com/paper/2005.01082/) (2020)
- [Data-Driven LQR Control Design](https://mlsanity.com/paper/1807.03263/) (2018)
- [Regularized and Distributionally Robust Data-Enabled Predictive Control](https://mlsanity.com/paper/1903.06804/) (2019)

## Abstract (arXiv)

We consider the online control problem with an unknown linear dynamical system in the presence of adversarial perturbations and adversarial convex loss functions. Although the problem is widely studied in model-based control, it remains unclear whether data-driven approaches, which bypass the system identification step, can solve the problem. In this work, we present a novel data-driven online adaptive control algorithm to address this online control problem. Our algorithm leverages the behavioral systems theory to learn a non-parametric system representation and then adopts a perturbation-based controller updated by online gradient descent. We prove that our algorithm guarantees an tmO(T2/3) regret bound with high probability, which matches the best-known regret bound for this problem. Furthermore, we extend our algorithm and performance guarantee to the cases with output feedback.