Abstract
Stochastic approximation is a recursive procedure to seek for a solution of an unknown nonlinear equation based on random noise corrupted residuals. This paper presents an upper bound of the expected squared estimation error of stochastic approximation in finite samples of the measurements. The bound is given as an affine function of the squared error of the initial candidate of the solution with parameters. Once the parameters are specified, the necessary number of the measurements can readily be computed in advance of execution of the procedure, which establishes a rigorous stopping rule for stochastic approximation.
