  In this work, we first show that the problem of parameter identification is
often ill-conditioned and lacks the persistence of excitation required for the
convergence of online learning schemes. To tackle these challenges, we
introduce the notion of optimal and greedy excitation sets which contain data
points with sufficient richness to aid in the identification task. We then
present the greedy excitation set-based recursive least squares algorithm to
alleviate the problem of the lack of persistent excitation, and prove that the
iterates generated by the proposed algorithm minimize an auxiliary weighted
least squares cost function. When data points are generated from time-varying
parameters, online estimators tend to underfit the true parameter trajectory,
and their predictability deteriorates. To tackle this problem, we propose a
memory resetting scheme leveraging change point detection techniques. Finally,
we illustrate the performance of the proposed algorithms via several numerical
case studies to learn the (time-varying) parameters of networked epidemic
dynamics, and compare it with results obtained using conventional approaches.
