Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation
- 1 October 1998
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 43 (10) , 1480-1484
- https://doi.org/10.1109/9.720513
Abstract
The simultaneous perturbation stochastic approximation (SPSA) algorithm has attracted considerable attention for challenging optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo process. The objective is to minimize the mean square error of the estimate. The authors also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector is found to be a symmetric Bernoulli in both cases. The authors end the paper with a numerical study related to the area of experiment design.Keywords
This publication has 8 references indexed in Scilit:
- Transfer optimization via simultaneous perturbation stochastic approximationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2005
- Comparative study of stochastic algorithms for system optimization based on gradient approximationsIEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 1997
- On the use of an SPSA-based model-free controller in quality improvementAutomatica, 1995
- A learning rule of neural networks via simultaneous perturbation and its hardware implementationNeural Networks, 1995
- A more efficient global optimization algorithm based on Styblinski and TangNeural Networks, 1994
- Multivariate stochastic approximation using a simultaneous perturbation gradient approximationIEEE Transactions on Automatic Control, 1992
- Stochastic Approximation Methods for Constrained and Unconstrained SystemsPublished by Springer Nature ,1978
- STOCHASTIC APPROXIMATIONPublished by Elsevier ,1971