Central limit theorems for stochastic optimization algorithms using infinitesimal perturbation analysis

Discrete Event Dynamic Systems: Theory and Applications

Volumn 10, Issue 1, 2000, Pages 5-32

  Tang, Qian Y U ^a   L'Ecuyer, Pierre ^a   Chen, Han F U ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; QUEUEING THEORY; RANDOM PROCESSES; THEOREM PROVING;

CENTRAL LIMIT THEOREMS; INFINITESIMAL PERTURBATION ANALYSIS; RECURSIVE ESTIMATION; STOCHASTIC APPROXIMATION;

OPTIMIZATION;

EID: 0033885975     PISSN: 09246703     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008347431468     Document Type: Article

References (40)

1. Asmussen, S. 1987. Applied Probability and Queues. New York: John Wiley and Sons.
2. Chen, H. F. 1993. Asymptotic efficient stochastic approximation. Stochastics and Stochastics Reports 45: 1-16.
3. Chen, H. F. 1994. Stochastic approximation and its new applications. Proc. 1994 Hong Kong International Workshop on New Directions in Control and Manufacturing, pp. 2-12.
4. Chen, H. F., and Zhu, Y. M. 1996. Stochastic Approximation. Shanghai Scientific and Technological Publishers.
5. Chong, E. K. P., and Ramadge, P. J. 1992. Convergence of recursive optimization algorithms using infinitesimal perturbation analysis estimates. Discrete Event Dynamic Systems: Theory and Appl. 1: 339-372.
6. Chong, E. K. P., and Ramadge, P. J. 1993. Optimization of queues using an infinitesimal perturbation analysis-based stochastic algorithm with general updates times. SIAM J. Contr. Optim. 31: 698-732.
7. Chong, E. K. P., and Ramadge, P. J. 1994. Stochastic optimization of regenerative systems using infinitesimal perturbation analysis. IEEE Trans. Automat. Contr. AC-39: 1400-1410.
8. Chow, Y. S. 1965. Local convergence of martingale and the law of large numbers. Ann. Math. Stat. 36: 552-558.
9. Chow, Y. S., and Teicher, H. 1988. Probability Theory: Independence, Interchangeability, Martingale, second edition. New York: Springer-Verlag.
10. Fu, M. C. 1990. Convergence of a stochastic approximation algorithm for the GI/G/1 queue using infinitesimal perturbation analysis. J. of Optim. Theory and Appl. 65: 149-160.
11. Fu, M. C., and Ho, Y. C. 1988. Using perturbation analysis for gradient estimation, averaging, and updating in a stochastic approximation algorithm. Proc. of the Winter Simulation Conference, pp. 509-517.
12. Glasserman, P. 1991. Gradient Estimation via Perturbation Analysis. Boston: Kluwer.
13. Glynn, P. W., and Whitt, W. 1992. The asymptotic efficiency of simulation estimators. Operations research 40: 505-520.
14. Gut, A. 1988. Stopped Random Walks: Limit Theorems and Applications. New York: Springer-Verlag.
15. Hall, P., and Heyde, C. C., 1980. Martingale Limit Theory and Its Application. New York: Acad. Press.
16. Ho, Y. C., and Cao, X. R. 1983. Perturbation analysis and optimization of queueing networks. J. Optimiz. Theory Appl. 40: 559-582.
17. Ho, Y. C., and Cao, X. R. 1991. Perturbation Analysis of Discrete Event Dynamic Systems. Boston: Kluwer.
18. Kushner, H. J., and Clark, D.S. 1978. Stochastic Approximation Methods for Constrained and Unconstrained Systems. New York: Springer.
19. Kushner, H. J., and Vázquez-Abad, F. J. 1996. Stochastic approximation methods for systems of interest over an infinite horizon. SIAM J. on Control and Optim. 34: 712-756.
20. L'Ecuyer, P. 1990. A unified view of the IPA, SF, and LR gradient estimation techniques. Management Science 36: 1364-1383.
21. L'Ecuyer, P., and Glynn, P. W. 1994. Stochastic optimization by simulation: convergence proofs for the GI/G/1 queue in steady-state. Management Sci. 40: 1562-1578.
22. L'Ecuyer, P., Giroux, N., and Glynn, P. W. 1994. Stochastic optimization by simulation: numerical experiments with the M/M/1 queue in steady-state. Management Sci. 40: 1245-1261.
23. L'Ecuyer, P., and Yin, G. 1998. Budget-dependent convergence rate of stochastic approximation. SIAM Journal on Optimization 8: 217-247.
24. Meketon, M. S. 1987. Optimization in simulation: a survey of recent results. Proc. of the 1987 Winter Simulation Conference, pp. 58-67.
25. Nevel'son, M. B., and Hasminsky, R. S. 1972. Stochastic approximation and recursive estimation. Translated in Amer. Math. Soc. Transl. Monographs, vol. 24. Providence.
26. Nummelin, E. 1981. Regeneration in tandem queues. Adv. Appl. Prob. 13: 221-230.
27. Polyak, B. T. 1990. New method of stochastic approximation type procedure. Automation and Remote Control 51: 937-946.
28. Robbins, H., and Monro, S. 1951. A stochastic approximation method. Ann. Math. Statist. 22: 400-407.
29. Sigman, K. 1990. Notes on the stability of closed queueing networks. J. Appl. Probab. 26: 678-682. 1990. Corrections. J. Appl. Probab. 27: 735.
30. Sigman, K. 1990. The stability of open queueing networks. Stoch. Processes and their Appls. 35: 11-25.
31. Stout, W. F. 1974. Almost Sure Convergence. New York: Academic Press.
32. Suri, R. 1989. Perturbation analysis: the state of the art and research issues explained via the GI/G/1 queue. Proc. IEEE 77: 114-137.
33. Suri, R., and Leung, Y. T. 1989. Single run optimization of discrete event simulations - An empirical study using the M/M/1 queue. IIE Transactions 21: 35-49.
34. Suri, R., and Zazanis, M.A. 1988. Perturbation analysis gives strongly consistent sensitivity estimates for the M/G/1 queue. Management Sci. 34: 39-64.
35. Tang, Q. Y., and Chen, H. F. 1994. Convergence of perturbation analysis based optimization algorithm with fixed number of customers period. Discrete Event Dynamic Systems: Theory and Appl. 4: 359-375.
36. Tang, Q. Y., Chen, H. F., and Han, Z. J. 1997. Convergence rates of Perturbation-Analysis-Robbins-Monro-Single-Run algorithms for single server queues. IEEE Trans. on Autom. Contr. 42: 1442-1447.
37. Tang, Q. Y., L'Ecuyer, P., and Chen, H. F. 1999. Asymptotic efficiency of perturbation analysis-based stochastic approximation with averaging. SIAM J. on Control and Optimization 37: 1822-1847.
38. Thorisson, H. (1985). The queue GI/G/1: finite moments of the cycle variables and uniform rates of convergence. Stoch. Processes and their Appl. 19: 85-99.
39. Wolff, R. 1989. Stochastic Modeling and the Theory of Queues. NJ: Prentice-Hall.
40. Yin, G. 1991. On extension of Polyak's averaging approach to stochastic approximation. Stochastics and Stochastics Reports 36: 245-264.