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Volumn 8, Issue 1, 1998, Pages 217-247

Budget-dependent convergence rate of stochastic approximation

Author keywords

Discrete event systems; Gradient estimate; Limit theorems; Rate of convergence; Stochastic approximation; Stochastic optimization

Indexed keywords


EID: 0032326765     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623495270723     Document Type: Article
Times cited : (56)

References (47)
  • 1
    • 0000813026 scopus 로고
    • A stochastic approximation algorithm with varying bounds
    • S. ANDRADÓTTIR, A stochastic approximation algorithm with varying bounds, Oper. Res., 43 (1995), pp. 1037-1048.
    • (1995) Oper. Res. , vol.43 , pp. 1037-1048
    • Andradóttir, S.1
  • 3
    • 0008976280 scopus 로고
    • Stochastic approximation: A generalization of the Robbins-Monro procedure
    • P. Mandl and M. Hušková. eds.
    • J. A. BATHER, Stochastic approximation: A generalization of the Robbins-Monro procedure, in Proc. 4th Prague Symposium Asymptotic Statist., P. Mandl and M. Hušková. eds., 1989, pp. 13-27.
    • (1989) Proc. 4th Prague Symposium Asymptotic Statist. , pp. 13-27
    • Bather, J.A.1
  • 4
    • 0011595015 scopus 로고
    • Stochastic approximation procedure with randomly varying truncations
    • H. F. CHEN AND Y. M. ZHU, Stochastic approximation procedure with randomly varying truncations, Scientic Sinica, 29 (1986), pp. 914-926.
    • (1986) Scientic Sinica , vol.29 , pp. 914-926
    • Chen, H.F.1    Zhu, Y.M.2
  • 5
    • 0000792517 scopus 로고
    • On a stochastic approximation method
    • K. L. CHUNG, On a stochastic approximation method, Annals of Mathematical Statistics, 25 (1954), pp. 463-483.
    • (1954) Annals of Mathematical Statistics , vol.25 , pp. 463-483
    • Chung, K.L.1
  • 7
    • 0001214703 scopus 로고
    • On asymptotic normality in stochastic approximation
    • V. FABIAN, On asymptotic normality in stochastic approximation, Annals of Mathematical Statistics, 39 (1968), pp. 1327-1332.
    • (1968) Annals of Mathematical Statistics , vol.39 , pp. 1327-1332
    • Fabian, V.1
  • 8
    • 0009685457 scopus 로고
    • Simulating discounted costs
    • B. L. FOX AND P. W. GLYNN, Simulating discounted costs, Management Science, 35 (1989), pp. 1297-1315.
    • (1989) Management Science , vol.35 , pp. 1297-1315
    • Fox, B.L.1    Glynn, P.W.2
  • 10
    • 0000728309 scopus 로고
    • Some guidelines and guarantees for common random numbers
    • P. GLASSERMAN AND D. D. YAO, Some guidelines and guarantees for common random numbers, Management Science, 38 (1992), pp. 884-908.
    • (1992) Management Science , vol.38 , pp. 884-908
    • Glasserman, P.1    Yao, D.D.2
  • 11
    • 0024478825 scopus 로고
    • A GSMP formalism for discrete event systems
    • P. W. GLYNN, A GSMP formalism for discrete event systems, Proc. of the IEEE, 77 (1989), pp. 14-23.
    • (1989) Proc. of the IEEE , vol.77 , pp. 14-23
    • Glynn, P.W.1
  • 12
    • 84976859194 scopus 로고
    • Likelihood ratio gradient estimation for stochastic systems
    • P. W. GLYNN, Likelihood ratio gradient estimation for stochastic systems, Communications of the ACM, 33 (1990), pp. 75-84.
    • (1990) Communications of the ACM , vol.33 , pp. 75-84
    • Glynn, P.W.1
  • 13
    • 0025491872 scopus 로고
    • Bias properties of budget constrained simulations
    • P. W. GLYNN AND P. HEIDELBERGER, Bias properties of budget constrained simulations, Oper. Res., 38 (1990), pp. 801-814.
    • (1990) Oper. Res. , vol.38 , pp. 801-814
    • Glynn, P.W.1    Heidelberger, P.2
  • 16
    • 0000174391 scopus 로고
    • The asymptotic efficiency of simulation estimators
    • P. W. GLYNN AND W. WHITT, The asymptotic efficiency of simulation estimators, Oper. Res., 40 (1992), pp. 505-520.
    • (1992) Oper. Res. , vol.40 , pp. 505-520
    • Glynn, P.W.1    Whitt, W.2
  • 17
    • 0002169596 scopus 로고
    • Monte-Carlo optimization of parametrized policies in a class of piecewise deterministic control systems arising in manufacturing flow control
    • A. HAURIE, P. L'ECUYER, AND CH. VAN DELFT, Monte-Carlo optimization of parametrized policies in a class of piecewise deterministic control systems arising in manufacturing flow control, Discrete Event Dynamic Systems: Theory and Appl., 4 (1994), pp. 87-111.
    • (1994) Discrete Event Dynamic Systems: Theory and Appl. , vol.4 , pp. 87-111
    • Haurie, A.1    L'Ecuyer, P.2    Van Delft, Ch.3
  • 18
    • 0040517153 scopus 로고
    • A modification of the Robbins-Monro process
    • J. KOMLÓS AND P. RÉVÉZ, A modification of the Robbins-Monro process, Studia Sci. Math. Hungar., 8 (1973), pp. 329-340.
    • (1973) Studia Sci. Math. Hungar. , vol.8 , pp. 329-340
    • Komlós, J.1    Révéz, P.2
  • 20
    • 0040517155 scopus 로고
    • Stochastic approximation methods for constrained and unconstrained systems
    • Springer-Verlag, Berlin, New York
    • H. J. KUSHNER AND D. S. CLARK, Stochastic Approximation Methods for Constrained and Unconstrained Systems, Appl. Math. Sci., 26, Springer-Verlag, Berlin, New York, 1978.
    • (1978) Appl. Math. Sci. , vol.26
    • Kushner, H.J.1    Clark, D.S.2
  • 21
    • 0018518852 scopus 로고
    • Rates of convergence for stochastic approximation type algorithms
    • H. J. KUSHNER AND H. HUANG, Rates of convergence for stochastic approximation type algorithms, SIAM J. Control Optim., 17 (1979), pp. 607-617.
    • (1979) SIAM J. Control Optim. , vol.17 , pp. 607-617
    • Kushner, H.J.1    Huang, H.2
  • 22
    • 0030105021 scopus 로고    scopus 로고
    • Stochastic approximation methods for systems over an infinite horizon
    • H. J. KUSHNER AND F. J. VÁZQUEZ-ABAD, Stochastic approximation methods for systems over an infinite horizon, SIAM J. Control Optim., 34 (1996), pp. 712-756.
    • (1996) SIAM J. Control Optim. , vol.34 , pp. 712-756
    • Kushner, H.J.1    Vázquez-Abad, F.J.2
  • 23
    • 0027627789 scopus 로고
    • Stochastic approximation with averaging of the iterates: Optimal asymptotic rate of convergence for general processes
    • H. J. KUSHNER AND J. YANG, Stochastic approximation with averaging of the iterates: Optimal asymptotic rate of convergence for general processes, SIAM J. Control Optim., 31 (1993), pp. 1045-1062.
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 1045-1062
    • Kushner, H.J.1    Yang, J.2
  • 25
    • 0026384154 scopus 로고
    • An overview of derivative estimation
    • IEEE Press, Piscataway, NJ, December
    • P. L'ECUYER, An overview of derivative estimation, in Proc. of the 1991 Winter Simulation Conference, IEEE Press, Piscataway, NJ, December 1991, pp. 207-217.
    • (1991) Proc. of the 1991 Winter Simulation Conference , pp. 207-217
    • L'Ecuyer, P.1
  • 26
    • 21144479912 scopus 로고
    • Convergence rates for steady-state derivative estimators
    • P. L'ECUYER, Convergence rates for steady-state derivative estimators, Ann. Oper. Res., 39 (1992), pp. 121-136.
    • (1992) Ann. Oper. Res. , vol.39 , pp. 121-136
    • L'Ecuyer, P.1
  • 27
    • 0001577860 scopus 로고
    • On the convergence rates of IPA and FDC derivative estimators
    • P. L'ECUYER AND G. PERRON, On the convergence rates of IPA and FDC derivative estimators. Oper. Res., 42 (1994), pp. 643-656.
    • (1994) Oper. Res. , vol.42 , pp. 643-656
    • L'Ecuyer, P.1    Perron, G.2
  • 28
    • 0000391011 scopus 로고
    • Stochastic optimization by simulation: Numerical experiments with the M/M/1 queue in steady-state
    • P. L'ECUYER, N. GIROUX, AND P. W. GLYNN, Stochastic optimization by simulation: Numerical experiments with the M/M/1 queue in steady-state, Management Science, 40 (1994), pp. 1245-1261.
    • (1994) Management Science , vol.40 , pp. 1245-1261
    • L'Ecuyer, P.1    Giroux, N.2    Glynn, P.W.3
  • 29
    • 0028546691 scopus 로고
    • Stochastic optimization by simulation: Convergence proofs for the GI/G/1 queue in steady-state
    • P. L'ECUYER AND P. W. GLYNN, Stochastic optimization by simulation: Convergence proofs for the GI/G/1 queue in steady-state, Management Science, 40 (1994), pp. 1562-1578.
    • (1994) Management Science , vol.40 , pp. 1562-1578
    • L'Ecuyer, P.1    Glynn, P.W.2
  • 32
    • 0010967230 scopus 로고
    • Stochastic approximation and recursive estimation
    • American Mathematical Society, Providence, RI
    • M. B. NEVEL'SON AND R. Z. KHASMINSKII, Stochastic Approximation and Recursive Estimation, Transl. Math. Monogr., 47. American Mathematical Society, Providence, RI, 1976.
    • (1976) Transl. Math. Monogr. , vol.47
    • Nevel'son, M.B.1    Khasminskii, R.Z.2
  • 33
    • 0008978039 scopus 로고
    • New method of stochastic approximation type
    • B. T. POLYAK, New method of stochastic approximation type, Avtomat. i Telemekh., 7 (1990), pp. 937-946. Translation in Automat. Remote Control, 51 (1991), pp. 937-946.
    • (1990) Avtomat. i Telemekh. , vol.7 , pp. 937-946
    • Polyak, B.T.1
  • 34
    • 84904774796 scopus 로고
    • Translation in
    • B. T. POLYAK, New method of stochastic approximation type, Avtomat. i Telemekh., 7 (1990), pp. 937-946. Translation in Automat. Remote Control, 51 (1991), pp. 937-946.
    • (1991) Automat. Remote Control , vol.51 , pp. 937-946
  • 35
    • 0026899240 scopus 로고
    • Acceleration of stochastic approximation by averaging
    • B. T. POLYAK AND A. B. JUDITSKY, Acceleration of stochastic approximation by averaging, SIAM J. Control Optim., 30 (1992), pp. 838-855.
    • (1992) SIAM J. Control Optim. , vol.30 , pp. 838-855
    • Polyak, B.T.1    Juditsky, A.B.2
  • 37
    • 0010921719 scopus 로고
    • Almost-sure approximation to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise
    • R. RUPPERT, Almost-sure approximation to the Robbins-Monro and Kiefer-Wolfowitz processes with dependent noise, Annals Probab., 10 (1982), pp. 178-187.
    • (1982) Annals Probab. , vol.10 , pp. 178-187
    • Ruppert, R.1
  • 38
    • 0001846920 scopus 로고
    • Handbook in sequential analysis
    • B. K. Ghosh and P. K. Sen. eds., Marcel Dekker, New York
    • R. RUPPERT, Handbook in sequential analysis, in Stochastic Approximation, B. K. Ghosh and P. K. Sen. eds., Marcel Dekker, New York, 1991, pp. 503-529.
    • (1991) Stochastic Approximation , pp. 503-529
    • Ruppert, R.1
  • 40
    • 0027608135 scopus 로고
    • A review of regenerative processes
    • K. SIGMAN AND R. W. WOLFF, A review of regenerative processes, SIAM Rev., 35 (1993), pp. 269-288.
    • (1993) SIAM Rev. , vol.35 , pp. 269-288
    • Sigman, K.1    Wolff, R.W.2
  • 42
    • 0025497275 scopus 로고
    • A stopping rule for the Robbins-Monro method
    • G. YIN, A stopping rule for the Robbins-Monro method, J. Optim. Theory Appl., 67 (1990), pp. 151-173.
    • (1990) J. Optim. Theory Appl. , vol.67 , pp. 151-173
    • Yin, G.1
  • 43
    • 0003254109 scopus 로고
    • On extensions of Polyak's averaging approach to stochastic approximation
    • G. YIN, On extensions of Polyak's averaging approach to stochastic approximation, Stochastics, 36 (1992), pp. 245-264.
    • (1992) Stochastics , vol.36 , pp. 245-264
    • Yin, G.1
  • 44
    • 0039924236 scopus 로고
    • On a class of stochastic optimization algorithms with applications to manufacturing models
    • H. P. W. W. G. Müller and A. A. Zhigljavsky, eds., Physica-Verlag, Heidelberg
    • G. YIN, H. YAN, AND X. LOU, On a class of stochastic optimization algorithms with applications to manufacturing models, in Proceedings of the Third Model-Oriented Data Analysis, H. P. W. W. G. Müller and A. A. Zhigljavsky, eds., Physica-Verlag, Heidelberg, 1993, pp. 213-226.
    • (1993) Proceedings of the Third Model-oriented Data Analysis , pp. 213-226
    • Yin, G.1    Yan, H.2    Lou, X.3
  • 45
    • 0003013920 scopus 로고
    • Asymptotically optimal rate of convergence of smoothed stochastic recursive algorithms
    • G. YIN AND K. YIN, Asymptotically optimal rate of convergence of smoothed stochastic recursive algorithms, Stochastics, 47 (1994), pp. 21-46.
    • (1994) Stochastics , vol.47 , pp. 21-46
    • Yin, G.1    Yin, K.2
  • 46
    • 0024649443 scopus 로고
    • Almost sure convergence of stochastic approximation algorithms with non-additive noise
    • G. YIN AND Y. M. ZHU, Almost sure convergence of stochastic approximation algorithms with non-additive noise, Internat. J. Control, 47 (1989), pp. 1361-1376.
    • (1989) Internat. J. Control , vol.47 , pp. 1361-1376
    • Yin, G.1    Zhu, Y.M.2
  • 47
    • 0011394477 scopus 로고
    • Convergence rates of finite-difference sensitivity estimates stochastic systems
    • M. A. ZAZANIS AND R. SURI, Convergence rates of finite-difference sensitivity estimates stochastic systems, Oper. Res., 41 (1993), pp. 694-703.
    • (1993) Oper. Res. , vol.41 , pp. 694-703
    • Zazanis, M.A.1    Suri, R.2


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