  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.
