# Hidden Convexity in Active Learning: A Convexified Online Input Design for ARX Systems

arXiv: https://arxiv.org/abs/2509.03257 · HTML: https://mlsanity.com/paper/2509.03257/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2025.

## Built on by (most cited first, 2 of 2)

- [High Effort, Low Gain: Fundamental Limits of Active Learning for Linear Dynamical Systems](https://mlsanity.com/paper/2509.11907/) (2025)
- [Optimal Centered Active Excitation in Linear System Identification](https://mlsanity.com/paper/2604.05518/) (2026)

## Abstract (arXiv)

The goal of this work is to accelerate the identification of an unknown ARX system from trajectory data through online input design. Specifically, we present an active learning algorithm that sequentially selects the input to excite the system according to an experiment design criterion using the past measured data. The adopted criterion yields a non-convex optimization problem, but we provide an exact convex reformulation allowing to find the global optimizer in a computationally tractable way. Moreover, we give sample complexity bounds on the estimation error due to the stochastic noise. Numerical studies showcase the effectiveness of our algorithm and the benefits of the convex reformulation.