Stochastic Approximation with Two Time Scales: The General Case

TL;DR

This paper analyzes two time scale stochastic approximation algorithms, especially focusing on cases where the iterates may not necessarily converge, expanding understanding of their behavior in more general settings.

Contribution

It provides a comprehensive analysis of two time scale stochastic approximation without the assumption of convergence of the iterates.

Findings

Analysis of convergence properties under broader conditions

Conditions for stability of the algorithms

Insights into non-convergent behaviors

Abstract

Two time scale stochastic approximation is analyzed when the iterates on either or both time scales do not necessarily converge.