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Efficiency of the stochastic approximation method

The practical aspect of the stochastic approximation method (SA) is studied. Specifically, we investigated the efficiency depending on the coefficients that generate the step length in optimization algorithm, as well as the efficiency depending on the type and the level of the corresponding noise. This paper provides suggestions how to choose already mentioned coefficients, in order to achieve better performance of the stochastic approximation algorithm. | Yugoslav Journal of Operations Research 22 (2012), Number 1, 131-140 DOI:10.2298/YJOR101124003J EFFICIENCY OF THE STOCHASTIC APPROXIMATION METHOD* M. JAPUNDŽIĆ Higher School of Professional Business Studies, Novi Sad, Serbia milos.japundzic@gmail.com Received: November 2010 / Accepted: September 2011 Abstract: The practical aspect of the stochastic approximation method (SA) is studied. Specifically, we investigated the efficiency depending on the coefficients that generate the step length in optimization algorithm, as well as the efficiency depending on the type and the level of the corresponding noise. Efficiency is measured by the mean values of the objective function at the final estimates of the algorithm, over the specified number of replications. This paper provides suggestions how to choose already mentioned coefficients, in order to achieve better performance of the stochastic approximation algorithm. Keywords: Stochastic approximation, step length, efficiency of the stochastic methods, noise. MSC: 49K45, 62L20, 90C15 1. INTRODUCTION There have been countless applications of the stochastic approximation method, in the period greater than a half century, since the seminal publication of Robbins and Monro [7] appeared. Some areas include neural network, simulation-based optimization, evolutionary algorithms, machine learning, experimental design, and signal processing applications such as noise cancellation and pattern recognition. This method is primarily used for solving systems of nonlinear equations in the presence of noisy measurements (1) g(θ) = 0, θ ∈ Θ ⊆ Rn * Some results contained in this paper were first published in the author’s MSc thesis [4]. 132 M. Japundžić / Efficiency of the Stochastic Approximation Method where is g(θ) ∈ Rn. So, the problem of interest is a typical nonlinear system of n equations with n unknowns, based on noisy measurements of g(θ) in the form Y(θ) = g(θ)+ e(θ), (2) where e(θ) represents the noise term. The problem (1)