# Achieving widetildeO(1/ε) Sample Complexity for Bilinear Systems Identification under Bounded Noises

arXiv: https://arxiv.org/abs/2603.20819 · HTML: https://mlsanity.com/paper/2603.20819/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 21 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [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 Sample Identification of Bilinear Dynamical Systems](https://mlsanity.com/paper/2208.13915/) (2022)
- [Set Membership identification of linear systems with guaranteed simulation accuracy](https://mlsanity.com/paper/2001.07628/) (2020)
- [Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guarantees](https://mlsanity.com/paper/2411.00656/) (2024)
- [Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2309.14648/) (2023)
- [CLOSURE: Fast Quantification of Pose Uncertainty Sets](https://mlsanity.com/paper/2403.09990/) (2024)
- [Online Adversarial Stabilization of Unknown Networked Systems](https://mlsanity.com/paper/2203.02630/) (2022)
- [Finite Sample Identification of Partially Observed Bilinear Dynamical Systems](https://mlsanity.com/paper/2501.07652/) (2025)
- [On the Sample Complexity of Set Membership Estimation for Linear Systems with Disturbances Bounded by Convex Sets](https://mlsanity.com/paper/2406.00574/) (2024)
- [System Identification Under Bounded Noise: Optimal Rates Beyond Least Squares](https://mlsanity.com/paper/2503.16817/) (2025)
- [Dual adaptive MPC using an exact set-membership reformulation](https://mlsanity.com/paper/2211.16300/) (2022)
- [A finite-sample bound for identifying partially observed linear switched systems from a single trajectory](https://mlsanity.com/paper/2503.13766/) (2025)

## Abstract (arXiv)

This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Our analysis considers trajectory-dependent regressors and allows marginally stable dynamics with polynomial mean-square state growth. We prove that the diameter of the feasible parameter set shrinks with sample complexity widetildemathcal O(1/ε) where ε is the estimation error. Simulation supports the theory and illustrates the advantage of the proposed estimator for uncertainty quantification.