Convergence rate of stochastic approximation algorithms in the degenerate case

SIAM Journal on Control and Optimization

Volumn 36, Issue 1, 1998, Pages 100-114

  Chen, Han Fu ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

Convergence rate; Stochastic approximation

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; RANDOM PROCESSES;

STOCHASTIC APPROXIMATION (SA);

APPROXIMATION THEORY;

EID: 0031647921     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012995281730     Document Type: Article

References (10)

1. H. ROBBINS AND S. MONRO, A stochastic approximation method, Ann. Math. Statist., 22 (1951), pp. 400-407.
2. M. B. NEVELSON AND R. Z. HASMINSKII, Stochastic Approximation and Recursive Estimation, Amer. Math. Soc. Transl. Math. Monographs 47, 1976.
3. H. J. KUSHNER AND D. S. CLARK, Stochastic Approximation for Constrained and Unconstrained Systems, Springer-Verlag, New York, 1978.
4. H.-F. CHEN, Stochastic approximation and its new applications, in Proc. 1994 Hong Kong International Workshop on New Directions of Control and Manufacturing, 1994, pp. 2-12.
5. L. LJUNG, G. PFLUG, AND H. WALK, Stochastic Approximation of Random Systems, Birkhäuser, Basel, 1992, pp. 71-76.
6. H.-F. CHEN, T. DUNCAN, AND B. PASIK-DUNCAN, On Ljung's approach to system parameter identification, in 10th IFAC Symposium on Systems Identification, Vol. 2, preprint, M. Blanke and T. Söderström, eds., Copenhagen, 1994, pp. 667-671.
7. H.-F. CHEN, Recursive Estimation and Control for Stochastic Systems, John Wiley, New York, 1985.
8. I. J. WANG, E. K. P. CHONG, AND S. R. KULKARNI, Equivalent necessary and sufficient conditions on noise sequences for stochastic approximation algorithms, Adv. in Appl. Probab., accepted for publication.
9. S. R. KULKARNI AND C. HORN, Convergence of the Robbins-Monro algorithm under arbitrary disturbances, in Proc. of 32nd Conf. on Decision and Control, 1993, pp. 537-538.
10. S. R. KULKARNI AND C. HORN, Alternative approach and conditions for convergence of stochastic approximation algorithms, in Proc. 34th Conf. on Decision and Control, New Orleans, IEEE Control Systems Society, 1995.