# A least-square method for non-asymptotic identification in linear switching control

arXiv: https://arxiv.org/abs/2404.08120 · HTML: https://mlsanity.com/paper/2404.08120/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 11 Apr 2024.

## Builds on (most cited first, 11 of 11)

- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Learning with little mixing](https://mlsanity.com/paper/2206.08269/) (2022)
- [A Tutorial on the Non-Asymptotic Theory of System Identification](https://mlsanity.com/paper/2309.03873/) (2023)
- [A New Approach to Learning Linear Dynamical Systems](https://mlsanity.com/paper/2301.09519/) (2023)
- [Online switching control with stability and regret guarantees](https://mlsanity.com/paper/2301.08445/) (2023)
- [Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part I](https://mlsanity.com/paper/2212.14511/) (2022)

## Built on by (most cited first, 1 of 1)

- [Online Learning for Supervisory Switching Control](https://mlsanity.com/paper/2603.14762/) (2026)

## Abstract (arXiv)

The focus of this paper is on linear system identification in the setting where it is known that the underlying partially-observed linear dynamical system lies within a finite collection of known candidate models. We first consider the problem of identification from a given trajectory, which in this setting reduces to identifying the index of the true model with high probability. We characterize the finite-time sample complexity of this problem by leveraging recent advances in the non-asymptotic analysis of linear least-square methods in the literature. In comparison to the earlier results that assume no prior knowledge of the system, our approach takes advantage of the smaller hypothesis class and leads to the design of a learner with a dimension-free sample complexity bound. Next, we consider the switching control of linear systems, where there is a candidate controller for each of the candidate models and data is collected through interaction of the system with a collection of potentially destabilizing controllers. We develop a dimension-dependent criterion that can detect those destabilizing controllers in finite time. By leveraging these results, we propose a data-driven switching strategy that identifies the unknown parameters of the underlying system. We then provide a non-asymptotic analysis of its performance and discuss its implications on the classical method of estimator-based supervisory control.