Sample Complexity Lower Bounds for Linear System Identification

03/25/2019
by   Yassir Jedra, et al.
0

This paper establishes problem-specific sample complexity lower bounds for linear system identification problems. The sample complexity is defined in the PAC framework: it corresponds to the time it takes to identify the system parameters with prescribed accuracy and confidence levels. By problem-specific, we mean that the lower bound explicitly depends on the system to be identified (which contrasts with minimax lower bounds), and hence really captures the identification hardness specific to the system. We consider both uncontrolled and controlled systems. For uncontrolled systems, the lower bounds are valid for any linear system, stable or not, and only depend of the system finite-time controllability gramian. A simplified lower bound depending on the spectrum of the system only is also derived. In view of recent finitetime analysis of classical estimation methods (e.g. ordinary least squares), our sample complexity lower bounds are tight for many systems. For controlled systems, our lower bounds are not as explicit as in the case of uncontrolled systems, but could well provide interesting insights into the design of control policy with minimal sample complexity.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/06/2019

Towards Testing Monotonicity of Distributions Over General Posets

In this work, we consider the sample complexity required for testing the...
research
11/18/2019

Comments on the Du-Kakade-Wang-Yang Lower Bounds

Du, Kakade, Wang, and Yang recently established intriguing lower bounds ...
research
03/17/2020

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 ...
research
04/02/2021

Linear Systems can be Hard to Learn

In this paper, we investigate when system identification is statisticall...
research
06/03/2019

Optimal Learning of Mallows Block Model

The Mallows model, introduced in the seminal paper of Mallows 1957, is o...
research
10/07/2020

Episodic Reinforcement Learning in Finite MDPs: Minimax Lower Bounds Revisited

In this paper, we propose new problem-independent lower bounds on the sa...
research
04/05/2012

Distribution-Dependent Sample Complexity of Large Margin Learning

We obtain a tight distribution-specific characterization of the sample c...

Please sign up or login with your details

Forgot password? Click here to reset