Error bound analysis of the least-mean-squares algorithm in linear models

摘要

Time-varying formulation is pervasive in dynamic control systems, where tracking parameters characterizing dynamic properties is central task. General conditions for exponential stability of such systems have been fully discussed in prior work of others. In this paper we build practical (computable) error bound analysis of the stochastic gradient algorithm when the loss function is time-dependent and quadratic in the parameters, as arising from standard linear regression model. The long term goal is to address this problem in general nonlinear models. This paper is the first step towards this aim.