DeepAI

# Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimator

We provide a new finite-time analysis of the estimation error of stable linear time-invariant systems under the Ordinary Least Squares (OLS) estimator. Specifically, we characterize the sufficient number of observed samples (the length of the observed trajectory) so that the OLS is (ε,δ)-PAC, i.e. yields an estimation error less than ε with probability at least 1-δ. We show that this number matches existing sample complexity lower bound [1,2] up to universal multiplicative factors (independent of (ε,δ), of the system and of the dimension). This paper hence establishes the optimality of the OLS estimator for stable systems, a result conjectured in [1]. Our analysis of the performance of the OLS estimator is simpler, sharper, and easier to interpret than existing analyses, but is restricted to stable systems. It relies on new concentration results for the covariates matrix.

• 7 publications
• 32 publications
03/25/2019

### Sample Complexity Lower Bounds for Linear System Identification

This paper establishes problem-specific sample complexity lower bounds f...
04/20/2019

### Learning Sparse Dynamical Systems from a Single Sample Trajectory

This paper addresses the problem of identifying sparse linear time-invar...
03/18/2022

### Finite-sample analysis of identification of switched linear systems with arbitrary or restricted switching

This work aims to derive a data-independent finite-sample error bound fo...
12/17/2019

### A Finite-Sample Deviation Bound for Stable Autoregressive Processes

In this paper, we study non-asymptotic deviation bounds of the least squ...
02/22/2018

### Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification

We prove that the ordinary least-squares (OLS) estimator attains nearly ...
03/21/2018

### Data-Driven Sparse System Identification

In this paper, we study the system identification porblem for sparse lin...
03/31/2022

### Learning from many trajectories

We initiate a study of supervised learning from many independent sequenc...