Title :
Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation
Author :
Sadegh, Payman ; Spall, James C.
Author_Institution :
Dept. of Math. Modeling, Tech. Univ., Lyngby, Denmark
Abstract :
The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for 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. We 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. We end the paper with a numerical study related to the area of experiment design
Keywords :
Monte Carlo methods; approximation theory; design of experiments; least mean squares methods; optimisation; perturbation techniques; random processes; Monte Carlo process; bounded symmetric region; experiment design; least mean square error; loss function measurements; optimal distribution; optimal random perturbations; random vector; simultaneous perturbation gradient approximation; simultaneous perturbation vector; stochastic approximation; symmetric Bernoulli distribution; Adaptive control; Cost function; Laboratories; Loss measurement; Mathematical model; Mean square error methods; Monte Carlo methods; Physics; Stochastic processes; Stochastic systems;
Conference_Titel :
American Control Conference, 1997. Proceedings of the 1997
Conference_Location :
Albuquerque, NM
Print_ISBN :
0-7803-3832-4
DOI :
10.1109/ACC.1997.609490