Multivariate stochastic approximation using a simultaneous perturbation gradient approximation
作者： J.C. Spall
DOI: 10.1109/9.119632
关键词: Minimax approximation algorithm 、 Asymptotic distribution 、 Approximation algorithm 、 Standard algorithms 、 Simultaneous perturbation stochastic approximation 、 Stochastic approximation 、 Mathematical analysis 、 Approximation error 、 Mathematics 、 Function approximation
摘要: The problem of finding a root the multivariate gradient equation that arises in function minimization is considered. When only noisy measurements are available, stochastic approximation (SA) algorithm for general Kiefer-Wolfowitz type appropriate estimating root. paper presents an SA based on simultaneous perturbation instead standard finite-difference Keifer-Wolfowitz procedures. Theory and numerical experience indicate can be significantly more efficient than algorithms large-dimensional problems. >
core.ac.uk
sci-hub.se 参考文章(28)
Y. Wardi, A stochastic steepest-descent algorithm Journal of Optimization Theory and Applications. ,vol. 59, pp. 307- 323 ,(1988) , 10.1007/BF00938315
George N. Saridis, Self-organizing control of stochastic systems ,(1977)
Larry Goldstein, On the choice of step size in the Robbins-Monro procedure Statistics & Probability Letters. ,vol. 6, pp. 299- 303 ,(1988) , 10.1016/0167-7152(88)90003-X
Julius R. Blum, Multidimensional Stochastic Approximation Methods Annals of Mathematical Statistics. ,vol. 25, pp. 737- 744 ,(1954) , 10.1214/AOMS/1177728659
Lennart Ljung, Strong Convergence of a Stochastic Approximation Algorithm Annals of Statistics. ,vol. 6, pp. 680- 696 ,(1978) , 10.1214/AOS/1176344212
H. J. Kushner, T. Gavin, Extensions of Kestin's Adaptive Stochastic Approximation Method, Annals of Statistics. ,vol. 1, pp. 851- 861 ,(1973) , 10.1214/AOS/1176342506
R. H. Shumway, D. E. Olsen, L. J. Levy, Estimation and tests of hypotheses for the initial mean and covariance in the kalman filter model Communications in Statistics-theory and Methods. ,vol. 10, pp. 1625- 1641 ,(1981) , 10.1080/03610928108828137
Yuri Ermoliev, Stochastic quasigradient methods and their application to system optimization Stochastics An International Journal of Probability and Stochastic Processes. ,vol. 9, pp. 1- 36 ,(1983) , 10.1080/17442508308833246
Harry Kesten, Accelerated Stochastic Approximation Annals of Mathematical Statistics. ,vol. 29, pp. 41- 59 ,(1958) , 10.1214/AOMS/1177706705
NADAV BERMAN, ARIE FEUER, ELIAS WAHNON, Convergence analysis of smoothed stochastic gradient-type algorithm International Journal of Systems Science. ,vol. 18, pp. 1061- 1078 ,(1987) , 10.1080/00207728708964032