On epsilon-optimality of the pursuit learning algorithm

TL;DR

This paper provides a theoretical analysis of the pursuit learning algorithm, emphasizing the importance of a decreasing tuning parameter for convergence, and fills gaps in existing convergence proofs.

Contribution

It offers a rigorous proof of probabilistic convergence for pursuit learning with a vanishing tuning parameter, addressing a gap in prior theoretical work.

Findings

Convergence is guaranteed with a decreasing tuning parameter.

Existing proofs had gaps that are now filled.

Highlights the importance of parameter tuning in pursuit learning.

Abstract

Estimator algorithms in learning automata are useful tools for adaptive, real-time optimization in computer science and engineering applications. This paper investigates theoretical convergence properties for a special case of estimator algorithms: the pursuit learning algorithm. In this note, we identify and fill a gap in existing proofs of probabilistic convergence for pursuit learning. It is tradition to take the pursuit learning tuning parameter to be fixed in practical applications, but our proof sheds light on the importance of a vanishing sequence of tuning parameters in a theoretical convergence analysis.