On the choice of random directions for stochastic approximation algorithms

IEEE Transactions on Automatic Control

Volumn 51, Issue 3, 2006, Pages 476-481

  Theiler, James ^a   Alper, Jarod ^a,b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Finite difference; Random direction; Simultaneous perturbation; Stochastic approximation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ASYMPTOTIC STABILITY; FINITE DIFFERENCE METHOD; NORMAL DISTRIBUTION; OPTIMIZATION; RANDOM PROCESSES;

BERNOULLI DISTRIBUTION; RANDOM DIRECTION; STOCHASTIC APPROXIMATION ALGORITHMS;

STOCHASTIC CONTROL SYSTEMS;

EID: 33644998505     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.864195     Document Type: Article

References (9)

1. H. Robbins and S. Monro, "A stochastic approximation method," Ann. Math. Stat., vol. 22, pp. 400-407, 1951.
2. J. Kiefer and J. Wolfowitz, "Stochastic estimation of the maximum of a regression function," Ann. Math. Stat., vol. 23, pp. 462-466, 1952.
3. J. R. Blum, "Multidimensional stochastic approximation methods," Ann. Math. Stat., vol. 25, pp. 737-744, 1954.
4. J. C. Spall, "Multivariate stochastic approximation using a simultaneous perturbation gradient approximation," IEEE Trans. Autom. Control, vol. 37, no. 3, pp. 332-341, Mar. 1992.
5. P. Sadegh and J. C. Spall, "Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation," in Proc. Amer. Control Conf., Albuquerque, NM, Jun. 4-6, 1997, pp. 3582-3586.
6. D. C. Chin, "Comparative study of stochastic algorithms for system optimization based on gradient approximation," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 27, no. 2, pp. 244-249, Apr. 1997.
7. J. C. Spall, "Implementation of the simultaneous perturbation algorithm for stochastic optimization," IEEE Trans. Aerospace Electron. Syst., vol. 34, no. 3, pp. 817-823, Jul. 1998.
8. V. Fabian, "On asymptotic normality in stochastic approximation," Ann. Math. Stat., vol. 39, pp. 1327-1332, 1968.
9. L. Gerencsér, "Convergence rate of moments in stochastic approximation with simultaneous perturbation gradient approximation and resetting," IEEE Trans. Autom. Control, vol. 44, no. 5, pp. 894-905, May 1999.