# Optimal Centered Active Excitation in Linear System Identification

arXiv: https://arxiv.org/abs/2604.05518 · HTML: https://mlsanity.com/paper/2604.05518/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## 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)
- [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 without Concentration](https://mlsanity.com/paper/1401.0304/) (2014)
- [Active Learning for Identification of Linear Dynamical Systems](https://mlsanity.com/paper/2002.00495/) (2020)
- [Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimator](https://mlsanity.com/paper/2003.07937/) (2020)
- [Task-Optimal Exploration in Linear Dynamical Systems](https://mlsanity.com/paper/2102.05214/) (2021)
- [Approximating the nearest stable discrete-time system](https://mlsanity.com/paper/1802.08033/) (2018)
- [Hidden Convexity in Active Learning: A Convexified Online Input Design for ARX Systems](https://mlsanity.com/paper/2509.03257/) (2025)
- [High Effort, Low Gain: Fundamental Limits of Active Learning for Linear Dynamical Systems](https://mlsanity.com/paper/2509.11907/) (2025)

## Abstract (arXiv)

We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity while allowing for efficient computation of an estimate of a system matrix. More specifically, we first establish lower bounds of the sample complexity for any active learning algorithm to attain the prescribed accuracy and confidence levels. Next, we derive a sample complexity upper bound of the proposed algorithm, which matches the lower bound for any algorithm up to universal factors. Our tight bounds are easy to interpret and explicitly show their dependence on the system parameters such as the state dimension.