Volume 1, Issue 4
A Stochastic Approximation Frame Algorithm with Adaptive Directions

Zi Xu & Yu-Hong Dai

Numer. Math. Theor. Meth. Appl., 1 (2008), pp. 460-474.

Published online: 2008-01

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  • Abstract

Stochastic approximation problem is to find some roots or extremum of a nonlinear function for which only noisy measurements of the function are available. The classical algorithm for stochastic approximation problem is the Robbins-Monro (RM) algorithm, which uses the noisy evaluation of the negative gradient direction as the iterative direction. In order to accelerate the RM algorithm, this paper gives a frame algorithm using adaptive iterative directions. At each iteration, the new algorithm goes towards either the noisy evaluation of the negative gradient direction or some other directions under some switch criteria. Two feasible choices of the criteria are proposed and two corresponding frame algorithms are formed. Different choices of the directions under the same given switch criterion in the frame can also form different algorithms. We also proposed the simultanous perturbation difference forms for the two frame algorithms. The almost surely convergence of the new algorithms are all established. The numerical experiments show that the new algorithms are promising.

  • Keywords

Stochastic approximation, conjugate gradient, adaptive directions.

  • AMS Subject Headings

O242.1

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-1-460, author = {}, title = {A Stochastic Approximation Frame Algorithm with Adaptive Directions}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2008}, volume = {1}, number = {4}, pages = {460--474}, abstract = {

Stochastic approximation problem is to find some roots or extremum of a nonlinear function for which only noisy measurements of the function are available. The classical algorithm for stochastic approximation problem is the Robbins-Monro (RM) algorithm, which uses the noisy evaluation of the negative gradient direction as the iterative direction. In order to accelerate the RM algorithm, this paper gives a frame algorithm using adaptive iterative directions. At each iteration, the new algorithm goes towards either the noisy evaluation of the negative gradient direction or some other directions under some switch criteria. Two feasible choices of the criteria are proposed and two corresponding frame algorithms are formed. Different choices of the directions under the same given switch criterion in the frame can also form different algorithms. We also proposed the simultanous perturbation difference forms for the two frame algorithms. The almost surely convergence of the new algorithms are all established. The numerical experiments show that the new algorithms are promising.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/9965.html} }
TY - JOUR T1 - A Stochastic Approximation Frame Algorithm with Adaptive Directions JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 460 EP - 474 PY - 2008 DA - 2008/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/9965.html KW - Stochastic approximation, conjugate gradient, adaptive directions. AB -

Stochastic approximation problem is to find some roots or extremum of a nonlinear function for which only noisy measurements of the function are available. The classical algorithm for stochastic approximation problem is the Robbins-Monro (RM) algorithm, which uses the noisy evaluation of the negative gradient direction as the iterative direction. In order to accelerate the RM algorithm, this paper gives a frame algorithm using adaptive iterative directions. At each iteration, the new algorithm goes towards either the noisy evaluation of the negative gradient direction or some other directions under some switch criteria. Two feasible choices of the criteria are proposed and two corresponding frame algorithms are formed. Different choices of the directions under the same given switch criterion in the frame can also form different algorithms. We also proposed the simultanous perturbation difference forms for the two frame algorithms. The almost surely convergence of the new algorithms are all established. The numerical experiments show that the new algorithms are promising.

Zi Xu & Yu-Hong Dai. (2020). A Stochastic Approximation Frame Algorithm with Adaptive Directions. Numerical Mathematics: Theory, Methods and Applications. 1 (4). 460-474. doi:
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