# Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems

arXiv: https://arxiv.org/abs/2108.11959 · HTML: https://mlsanity.com/paper/2108.11959/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 55 references that are in the map.
- First posted on arXiv 26 Aug 2021.

## Builds on (most cited first, 16 of 16)

- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [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)
- [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)
- [Finite Sample Analysis of Stochastic System Identification](https://mlsanity.com/paper/1903.09122/) (2019)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems](https://mlsanity.com/paper/2003.11227/) (2020)
- [Logarithmic Regret for Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [On Adaptive Linear-Quadratic Regulators](https://mlsanity.com/paper/1806.10749/) (2018)
- [Optimism-Based Adaptive Regulation of Linear-Quadratic Systems](https://mlsanity.com/paper/1711.07230/) (2017)
- [Certainty Equivalence is Efficient for Linear Quadratic Control](https://mlsanity.com/paper/1902.07826/) (2019)
- [Regret Minimization in Partially Observable Linear Quadratic Control](https://mlsanity.com/paper/2002.00082/) (2020)
- [Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting](https://mlsanity.com/paper/2003.05999/) (2020)

## Built on by (most cited first, 4 of 4)

- [A Tutorial on the Non-Asymptotic Theory of System Identification](https://mlsanity.com/paper/2309.03873/) (2023)
- [Thompson Sampling Achieves tilde O(√T) Regret in Linear Quadratic Control](https://mlsanity.com/paper/2206.08520/) (2022)
- [Efficient learning of hidden state LTI state space models of unknown order](https://mlsanity.com/paper/2202.01625/) (2022)
- [SCaLE: Switching Cost aware Learning and Exploration](https://mlsanity.com/paper/2601.09042/) (2026)

## Abstract (arXiv)

Autoregressive exogenous (ARX) systems are the general class of input-output dynamical systems used for modeling stochastic linear dynamical systems (LDS) including partially observable LDS such as LQG systems. In this work, we study the problem of system identification and adaptive control of unknown ARX systems. We provide finite-time learning guarantees for the ARX systems under both open-loop and closed-loop data collection. Using these guarantees, we design adaptive control algorithms for unknown ARX systems with arbitrary strongly convex or convex quadratic regulating costs. Under strongly convex cost functions, we design an adaptive control algorithm based on online gradient descent to design and update the controllers that are constructed via a convex controller reparametrization. We show that our algorithm has tildeO(√T) regret via explore and commit approach and if the model estimates are updated in epochs using closed-loop data collection, it attains the optimal regret of polylog(T) after T time-steps of interaction. For the case of convex quadratic cost functions, we propose an adaptive control algorithm that deploys the optimism in the face of uncertainty principle to design the controller. In this setting, we show that the explore and commit approach has a regret upper bound of tildeO(T2/3), and the adaptive control with continuous model estimate updates attains tildeO(√T) regret after T time-steps.