Efficiency of the stochastic approximation method

Authors

  • Miloš Japundžić Higher School of Professional Business Studies, Novi Sad

DOI:

https://doi.org/10.2298/YJOR101124003J

Keywords:

Stochastic approximation, step length, efficiency of the stochastic methods, noise

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.

References

Chung, K.L., "On a stochastic approximation method", Annals of Mathematical Statistics, 25 (1954) 463-483.

Fabian, V., "On asymptotic normality in stochastic approximation", Annals of Mathematical Statistics, 39 (1968) 1327-1332.

Fabian, V., "Stochastic Approximation", in: Optimizing Methods in Statistics, Academic Press, New York, 1971, 439-470.

Japundžić, M., "Efficiency of the modifications of deterministic methods in solving the stochastic optimization problem", MSc Thesis (in Serbian language), University of Novi Sad, Faculty of Natural Sciences and Mathematics, October 2010.

Kushner, H.J., Yin, G., Stochastic Approximation and Recursive Algorithms and Applications, Springer-Verlag, Second Edition, 2003.

Nevel’son, M.B., Has’minskii, R.Z., Stochastic Approximation and Recursive Estimation, American Mathematical Society, 1973.

Robbins, H., Monro, S., "A stochastic approximation method", Annals of Mathematical Statistics, 22 (1951) 400-407.

Sacks, J., "Asymptotic distribution of stochastic approximation procedures", Annals of Mathematical Statistics, 29 (1958) 373-405.

Spall, J.C., "Multivariate stochastic approximation using a simultaneous perturbation gradient approximation", IEEE Transactions on Automatic Control, 37 (1992) 332-341.

Spall, J.C., "Adaptive stochastic approximation by the simultaneous perturbation method", IEEE Transactions on Automatic Control, 45 (2000) 1839-1853.

Spall, J.C., Introduction to Stochastic Search and Optimization, Wiley-Interscience, New Jersey, 2003, 95-125.

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Published

2012-03-01

Issue

Section

Research Articles