Combining the Stochastic Counterpart and Stochastic Approximation Methods

Discrete Event Dynamic Systems: Theory and Applications

Volumn 7, Issue 1, 1997, Pages 5-28

  Dussault, Jean Pierre ^a   Labrecque, Donald ^b   L'Ecuyer, Pierre ^b   Rubinstein, Reuven Y ^c,d  

^a UNIVERSITÉ DE SHERBROOKE   (Canada)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^d EPFL   (Switzerland)

Author keywords

Optimization; Score function; Sensitivity analysis; Stochastic approximation; Stochastic counterpart

Indexed keywords

APPROXIMATION THEORY; COMBINATORIAL MATHEMATICS; CONVERGENCE OF NUMERICAL METHODS; MONTE CARLO METHODS; OPTIMIZATION; PARALLEL ALGORITHMS; PARAMETER ESTIMATION; PROBABILITY; SENSITIVITY ANALYSIS; SET THEORY;

DISCRETE EVENT SYSTEMS (DES); SCORE FUNCTION METHOD; STOCHASTIC COUNTERPART METHOD;

RANDOM PROCESSES;

EID: 0030786865     PISSN: 09246703     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008286324509     Document Type: Article

References (37)

1. Asmussen, S. and R. Y. Rubinstein (1992a). The efficiency and heavy traffic properties of the score function method for sensitivity analysis of queueing models. Advances in Applied Probability, 24, 172-201.
2. Asmussen, S. and R. Y. Rubinstein (1992b). Performance Evaluation for the Score Function Method in Sensitivity Analysis and Stochastic Optimization. International Workshop on Computer-Intensive Methods in Discrete Event Systems, Vienna, 1990, (G. Pflug ed.). Springer-Verlag, 1-12.
3. Asmussen, S., R. Y. Rubinstein, and C. Wang (1994). Estimating Rare Events via Likelihood Ratios: From M/M/1 Queues to Bottleneck Networks, Journal of Applied Probability, 31, 797-815.
4. Basa̧r, T. (1987). Relaxation techniques and asynchronous algorithms for on-line computation of non-cooperative equilibria, Journal of Economic Dynamics and Control, 11, 531-549.
5. Bertsekas, D. P. and J. N. Tsitsiklis (1989). Parallel and distributed computation: Numerical methods, Prentice-Hall.
6. Ermoliev, Y. M. (1983). Stochastic Quasigradient Methods and their Application to System Optimization, Stochastics, 9, 1-36.
7. Ermoliev, Y. M. and Gaivoronski, A. A. (1992). Stochastic Quasigradient Methods for Optimization of Discrete Event Systems, Annals of Operations Research, 39, 1-39.
8. Glasserman, P. (1991). Gradient Estimation via Perturbation Analysis, Kluwer Academic Press.
9. Glynn, P. W. and D. L. Iglehart (1989). Importance Sampling for Stochastic Simulations, Management Science, 35, 11, 1367-1392.
10. Glynn, P. W. (1990). Likelihood Ratio Gradient Estimation for Stochastic Systems, Communications of the ACM, 33, 10, 75-84.
11. Glynn, P. W., L'Ecuyer, P., and Adès, M. (1991). Gradient Estimation for Ratios, Proceedings of the 1991 Winter Simulation Conference, IEEE Press, 986-993.
12. Goldsman, D., Nelson, B., and Schmeiser, B. (1991). Methods for Selecting the best System, Proceedings of the 1991 Winter Simulation Conference, IEEE Press, 177-186.
13. Heidelberger, P., X.-R. Cao, M. A. Zazanis, and R. Suri (1988). "Convergence Properties of Infinitesimal Perturbation Analysis Estimates", Management Science, 34, 11, 1281-1302.
14. Kleijnen, J. P. C. and Van Groenendaal, W. (1992). Simulation: A Statistical Perspective, Wiley, Chichester.
15. Kushner, H. J. and D. S. Clark (1978). Stochastic Approximation Methods for Constrained and Unconstrained Systems, Springer-Verlag, Applied Math. Sciences, Vol. 26.
16. Law, A. M. and Kelton, W. D. (1991). Simulation Modeling and Analysis, second edition, McGraw-Hill.
17. L'Ecuyer, P. (1990). A unified view of the IPA, SF, and LR gradient estimation techniques. Management Science, 36, 1364-1384.
18. L'Ecuyer, P. (1992). Convergence rates for steady-state derivative estimator. Annals of Operations Research, 39, 121-136.
19. L'Ecuyer, P. (1993). Two Approaches for Estimating the Gradient in Functional Form, Proceedings of the 1993 Winter Simulation Conference, IEEE Press, 338-346.
20. L'Ecuyer, P. and G. Perron (1994). On the Convergence Rates of IPA and FDC Derivative Estimators. Operations Research 42, 643-656.
21. L'Ecuyer, P. and P. W. Glynn (1994). Stochastic Optimization by Simulation: Convergence Proofs for the GI/G/1 Queue in Steady-State. Management Science 40, 1562-1578.
22. L'Ecuyer, P., N. Giroux, and P. W. Glynn (1994). Stochastic Optimization by Simulation: Numerical Experiments for the M/M/1 Queue in Steady-State. Management Science 40, 1245-1261.
23. L'Ecuyer, P. and G. Yin (1994). Budget-Dependent Convergence Rate of Stochastic Approximation. To appear in SIAM Journal on Optimization.
24. Pflug, G. Ch. (1990). On-Line Optimization of Simulated Markov Processes. Mathematics of Operations Research 15, 381-395.
25. Pflug, G. Ch. (1992). Gradient Estimates for the Performance of Markov Chains and Discrete Event Processes. Annals of Operations Research 39, 173-194.
26. Plambeck, E. L., Fu, B.-R., Robinson, S. M., and Suri, R. (1993). Optimizing Performance Functions in Stochastic Systems. Submitted.
27. Polyak, B. T. and Juditsky, A. B. (1992). Acceleration of Stochastic Approximation by Averaging, SIAM J. on Control and Optimization 30, 4, 838-855.
28. Reiman, M. I. and A. Weiss (1989). Sensitivity analysis for simulations via likelihood ratios, Operations Research 37, 830-844.
29. Rubinstein, R. Y. (1976). A Monte Carlo method for estimating the gradient in a stochastic network. Unpublished manuscript, Technion, Haifa, Israel.
30. Rubinstein, R. Y. (1986). Monte Carlo Optimization Simulation and Sensitivity of Queueing Network, John Wiley & Sons, Inc., New York.
31. Rubinstein, R. Y. (1992). Monte Carlo Methods for performance evaluation, sensitivity analysis and optimization of stochastic systems, Encyclopedia of Computer Science and Technology (Kent ed.), Marcel Deker, Inc., Vol. 25, 211-233.
32. Rubinstein, R. Y. and A. Shapiro (1993). Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization via the Score Function Method, John Wiley & Sons.
33. Rubinstein, R. Y. and S. Uryas'ev (1994). On Relaxation Algorithms in Computation of Non-Cooperative Equilibria, IEEE Transactions on Automatic Control, AC-39, 6, 1263-1268.
34. Suri, R. and M. A. Zazanis (1988). Perturbation analysis gives strongly consistent sensitivity estimates for the M/G/1 queue, Management Science, 34, 1, 39-64.
35. Uryas'ev, S. P. (1992). A Stochastic Quasigradient Algorithm with Variable Metric, Annals of Operations Research, 39, 251-267.
36. Wolff, R. (1989). Stochastic Modeling and the Theory of Queues, Prentice-Hall.
37. Yang, W.-N. and Nelson, B. L. (1991). Using Common Random Numbers and Control Variates in Multiple-Comparison Procedures, Operations Research, 39, 4, 583-591.