On fixed gain recursive estimators with discontinuity in the parameters

TL;DR

This paper analyzes the tracking error of fixed gain stochastic approximation algorithms, accommodating non-Markovian processes and discontinuous update functions, under mixing conditions.

Contribution

It introduces a framework for estimating tracking error in fixed gain schemes with discontinuous updates and non-Markovian processes, expanding prior theoretical results.

Findings

Derived bounds on tracking error under mixing conditions

Extended analysis to discontinuous updating functions

Applicable to broader classes of stochastic approximation algorithms

Abstract

In this paper we estimate the tracking error of a fixed gain stochastic approximation scheme. The underlying process is not assumed Markovian, a mixing condition is required instead. Furthermore, the updating function may be discontinuous in the parameter.