Abstract
The adaptive Robbins-Monro stochastic approximation procedure is extended. Parameter convergence rate of the stochastic approximation procedure crucially depends on the gain coefficient which determines the increment of the parameter at each step. The adaptive Robbins-Monro procedure contains an algorithm to estimate the optimal gain. In this paper, an extension of this algorithm for the gain is proposed. We clarify the conditions which guarantee the convergence of the gain to the optimal one. Under these conditions, it becomes possible to improve the parameter convergence rate of the stochastic approximation procedure. An illustrative example is shown.
