Aspects on accelerated convergence in stochastic approximation schemes

So called accelerated convergence is an ingenuous idea to improve the asymptotic accuracy in stochastic approximation (gradient based) algorithms. The estimates obtained from the basic algorithm are subjected to a second round of averaging, which leads to optimal accuracy for estimates of time-invariant parameters. In this contribution some simple and approximate calculations are used to get some intuitive insight into these mechanisms. Of particular interest is to investigate the properties of accelerated convergence schemes in tracking situations