Implemented Optimal Algorithm of Passive Stochastic Approximation with Averaging along a Trajectory

The problem of finding a root of a regression equation is considered in passive stochastic approximation. An implemented (adaptive) version is proposed for the asymptotically optimal algorithm with averaging investigated earlier by the authors. This is based on the estimation of unknown parameters of the problem which are required when calculating the optimal value for the bandwidth. Convergence with probability 1 and in the mean square is proved for the estimates, as well as their optimality in terms of asymptotic normality.