# Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems

arXiv: https://arxiv.org/abs/2412.04157 · HTML: https://mlsanity.com/paper/2412.04157/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 37 references that are in the map.
- First posted on arXiv 5 Dec 2024.

## Builds on (most cited first, 19 of 19)

- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
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- [Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systems](https://mlsanity.com/paper/2002.08538/) (2020)
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- [Reinforcement Learning with Fast Stabilization in Linear Dynamical Systems](https://mlsanity.com/paper/2007.12291/) (2020)
- [Linear Systems can be Hard to Learn](https://mlsanity.com/paper/2104.01120/) (2021)
- [A Tutorial on Concentration Bounds for System Identification](https://mlsanity.com/paper/1906.11395/) (2019)
- [Finite Sample Identification of Bilinear Dynamical Systems](https://mlsanity.com/paper/2208.13915/) (2022)
- [Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guarantees](https://mlsanity.com/paper/2411.00656/) (2024)
- [Non-asymptotic System Identification for Linear Systems with Nonlinear Policies](https://mlsanity.com/paper/2306.10369/) (2023)
- [Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraints](https://mlsanity.com/paper/2209.07040/) (2022)
- [Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraints](https://mlsanity.com/paper/2304.00569/) (2023)

## Abstract (arXiv)

We investigate the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems. Specifically, we consider nonlinear systems with linearly parametrised uncertainty and additive i.i.d. process noise, in feedback with a control policy that is intentionally perturbed by an exploratory input. Assuming the open-loop dynamics satisfy a particular sub-exponential input-to-state growth property, and a region of the state space produces informative data, we establish non-asymptotic guarantees on the estimation error at times when the state trajectory evolves in this region. If the whole state space is informative, high-probability guarantees on the error hold for all times. Examples are provided where our results are useful for analysis beyond existing works.