# Non-asymptotic System Identification for Linear Systems with Nonlinear Policies

arXiv: https://arxiv.org/abs/2306.10369 · HTML: https://mlsanity.com/paper/2306.10369/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 17 Jun 2023.

## Builds on (most cited first, 20 of 20)

- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [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)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Learning nonlinear dynamical systems from a single trajectory](https://mlsanity.com/paper/2004.14681/) (2020)
- [Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systems](https://mlsanity.com/paper/2002.08538/) (2020)
- [Linear model predictive safety certification for learning-based control](https://mlsanity.com/paper/1803.08552/) (2018)
- [Safely Learning to Control the Constrained Linear Quadratic Regulator](https://mlsanity.com/paper/1809.10121/) (2018)
- [Learning with little mixing](https://mlsanity.com/paper/2206.08269/) (2022)
- [Learning the Linear Quadratic Regulator from Nonlinear Observations](https://mlsanity.com/paper/2010.03799/) (2020)
- [Online Optimal Control with Affine Constraints](https://mlsanity.com/paper/2010.04891/) (2020)
- [Stochastic Gradient Descent Learns State Equations with Nonlinear Activations](https://mlsanity.com/paper/1809.03019/) (2018)
- [Finite Sample Identification of Bilinear Dynamical Systems](https://mlsanity.com/paper/2208.13915/) (2022)
- [Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees](https://mlsanity.com/paper/2111.00411/) (2021)
- [Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended version](https://mlsanity.com/paper/1909.01813/) (2019)
- [A Control Barrier Perspective on Episodic Learning via Projection-to-State Safety](https://mlsanity.com/paper/2003.08028/) (2020)
- [Regret Analysis of Learning-Based MPC with Partially-Unknown Cost Function](https://mlsanity.com/paper/2108.02307/) (2021)

## Built on by (most cited first, 5 of 5)

- [Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2309.14648/) (2023)
- [On the Sample Complexity of Set Membership Estimation for Linear Systems with Disturbances Bounded by Convex Sets](https://mlsanity.com/paper/2406.00574/) (2024)
- [Online Identification of Stochastic Continuous-Time Wiener Models Using Sampled Data](https://mlsanity.com/paper/2403.05899/) (2024)
- [Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems](https://mlsanity.com/paper/2412.04157/) (2024)
- [Optimizing Digital Therapeutic Interventions: Online Learning under Endogenous Adherence](https://mlsanity.com/paper/2605.24261/) (2026)

## Abstract (arXiv)

This paper considers a single-trajectory system identification problem for linear systems under general nonlinear and/or time-varying policies with i.i.d. random excitation noises. The problem is motivated by safe learning-based control for constrained linear systems, where the safe policies during the learning process are usually nonlinear and time-varying for satisfying the state and input constraints. In this paper, we provide a non-asymptotic error bound for least square estimation when the data trajectory is generated by any nonlinear and/or time-varying policies as long as the generated state and action trajectories are bounded. This significantly generalizes the existing non-asymptotic guarantees for linear system identification, which usually consider i.i.d. random inputs or linear policies. Interestingly, our error bound is consistent with that for linear policies with respect to the dependence on the trajectory length, system dimensions, and excitation levels. Lastly, we demonstrate the applications of our results by safe learning with robust model predictive control and provide numerical analysis.