Error-In-Variables Methods for Efficient System Identification with Finite-Sample Guarantees

Abstract

This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by adapting the instrumental variable method and the bias compensation method, originally proposed for error-in-variables models, to our setting. We provide refined non-asymptotic analysis for both methods. Under mild conditions, our algorithms achieve superior sample complexities that match the best-known sample complexity for learning a fully observable system without observation noise.