Learning Dynamical Systems by Leveraging Data from Similar Systems

TL;DR

This paper introduces a method for improving linear system dynamics learning by incorporating data from similar auxiliary systems, providing finite sample bounds and a data-dependent approach to optimize the use of auxiliary data.

Contribution

It develops a weighted least squares framework that leverages auxiliary system data, offering finite sample error bounds and a data-dependent method to select optimal weights.

Findings

Auxiliary data reduces system identification error in noisy settings.

The method provides computable bounds based on prior knowledge.

Optimal weighting balances auxiliary data benefits and model differences.

Abstract

We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide finite sample error bounds of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems, such as upper bounds on noise levels and model difference, is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.