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Volumn 31, Issue 4, 2003, Pages 1260-1281

Accelerated randomized stochastic optimization

Author keywords

Asymptotic normality; Gradient estimation; Optimal rates of convergence; Randomization; Stochastic approximation; Stochastic optimization

Indexed keywords


EID: 0042859914     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1059655913     Document Type: Article
Times cited : (42)

References (20)
  • 1
    • 0000123608 scopus 로고
    • Asymptotic behaviour of a class of stochastic approximation procedures
    • BERGER, E. (1986). Asymptotic behaviour of a class of stochastic approximation procedures. Probab. Theory Related Fields 71 517-552.
    • (1986) Probab. Theory Related Fields , vol.71 , pp. 517-552
    • Berger, E.1
  • 2
    • 0000792515 scopus 로고
    • Multidimensional stochastic approximation methods
    • BLUM, J. R. (1954). Multidimensional stochastic approximation methods. Ann. Math. Statist. 25 737-744.
    • (1954) Ann. Math. Statist. , vol.25 , pp. 737-744
    • Blum, J.R.1
  • 3
    • 0011633314 scopus 로고
    • Lower rate of convergence for locating a maximum of a function
    • CHEN, H. (1988). Lower rate of convergence for locating a maximum of a function. Ann. Statist. 16 1330-1334.
    • (1988) Ann. Statist. , vol.16 , pp. 1330-1334
    • Chen, H.1
  • 5
    • 0031233853 scopus 로고    scopus 로고
    • Weighted means in stochastic approximation of minima
    • DIPPON, J. and RENZ, J. (1997). Weighted means in stochastic approximation of minima. SIAM J. Control Optim. 35 1811-1827.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 1811-1827
    • Dippon, J.1    Renz, J.2
  • 6
    • 0003219216 scopus 로고
    • Stochastic approximation of minima with improved asymptotic speed
    • FABIAN, V. (1967). Stochastic approximation of minima with improved asymptotic speed. Ann. Math. Statist. 38 191-200.
    • (1967) Ann. Math. Statist. , vol.38 , pp. 191-200
    • Fabian, V.1
  • 7
    • 0001214703 scopus 로고
    • On asymptotic normality in stochastic approximation
    • FABIAN, V. (1968). On asymptotic normality in stochastic approximation. Ann. Math. Statist. 39 1327-1332.
    • (1968) Ann. Math. Statist. , vol.39 , pp. 1327-1332
    • Fabian, V.1
  • 8
    • 0003361256 scopus 로고
    • Stochastic approximation]
    • (J. S. Rustagi, ed.) Academic Press, New York
    • FABIAN, V. (1971). Stochastic approximation. In Optimizing Methods in Statistics (J. S. Rustagi, ed.) 439-470. Academic Press, New York.
    • (1971) Optimizing Methods in Statistics , pp. 439-470
    • Fabian, V.1
  • 9
    • 0032657551 scopus 로고    scopus 로고
    • Convergence rate of moments in stochastic approximation with simultaneous perturbation gradient approximation and resetting
    • GERENCSÉR, L. (1999). Convergence rate of moments in stochastic approximation with simultaneous perturbation gradient approximation and resetting. IEEE Trans. Automat. Control 44 894-905.
    • (1999) IEEE Trans. Automat. Control , vol.44 , pp. 894-905
    • Gerencsér, L.1
  • 10
    • 0001079593 scopus 로고
    • Stochastic estimation of the maximum of a regression function
    • KIEFER, J. and WOLFOWITZ, J. (1952). Stochastic estimation of the maximum of a regression function. Ann. Math. Statist. 23 462-466.
    • (1952) Ann. Math. Statist. , vol.23 , pp. 462-466
    • Kiefer, J.1    Wolfowitz, J.2
  • 13
    • 0026899240 scopus 로고
    • Acceleration of stochastic approximation by averaging
    • POLYAK, B. T. and JUDITSKY, A. B. (1992). Acceleration of stochastic approximation by averaging. SIAM J. Control Optim. 30 838-855.
    • (1992) SIAM J. Control Optim. , vol.30 , pp. 838-855
    • Polyak, B.T.1    Juditsky, A.B.2
  • 14
    • 0025496781 scopus 로고
    • Optimal orders of accuracy for search algorithms of stochastic optimization
    • POLYAK, B. T. and TSYBAKOV, A. B. (1990). Optimal orders of accuracy for search algorithms of stochastic optimization. Problems Inform. Transmission 26 126-133.
    • (1990) Problems Inform. Transmission , vol.26 , pp. 126-133
    • Polyak, B.T.1    Tsybakov, A.B.2
  • 15
    • 0002686402 scopus 로고
    • A convergence theorem for nonnegative almost supermartingales and some applications
    • (J. S. Rustagi, ed.) Academic Press, New York
    • ROBBINS, H. and SIEGMUND, D. (1971). A convergence theorem for nonnegative almost supermartingales and some applications. In Optimizing Methods in Statistics (J. S. Rustagi, ed.) 233-257. Academic Press, New York.
    • (1971) Optimizing Methods in Statistics , pp. 233-257
    • Robbins, H.1    Siegmund, D.2
  • 16
    • 0001846920 scopus 로고
    • Stochastic approximation
    • (B. K. Ghosh and P. K. Sen, eds.) Dekker, New York
    • RUPPERT, D. (1991). Stochastic approximation. In Handbook of Sequential Analysis (B. K. Ghosh and P. K. Sen, eds.) 503-529. Dekker, New York.
    • (1991) Handbook of Sequential Analysis , pp. 503-529
    • Ruppert, D.1
  • 17
    • 0024169394 scopus 로고
    • A stochastic approximation algorithm for large-dimensional systems in the Kiefer-Wolfowitz setting
    • IEEE, New York
    • SPALL, J. C. (1988). A stochastic approximation algorithm for large-dimensional systems in the Kiefer-Wolfowitz setting. In Proc. Conference on Decision and Control 1544-1548. IEEE, New York.
    • (1988) Proc. Conference on Decision and Control , pp. 1544-1548
    • Spall, J.C.1
  • 18
    • 0026839090 scopus 로고
    • Multivariate stochastic approximation using a simultaneous perturbation gradient approximation
    • SPALL, J. C. (1992). Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Automat. Control. 37 332-341.
    • (1992) IEEE Trans. Automat. Control , vol.37 , pp. 332-341
    • Spall, J.C.1
  • 19
    • 0030737152 scopus 로고    scopus 로고
    • A one-measurement form of simultaneous perturbation stochastic approximation
    • SPALL, J. C. (1997). A one-measurement form of simultaneous perturbation stochastic approximation. Automatica J. IFAC 33 109-112.
    • (1997) Automatica J. IFAC , vol.33 , pp. 109-112
    • Spall, J.C.1
  • 20
    • 0000301473 scopus 로고
    • Limit behaviour of stochastic approximation processes
    • WALK, H. (1988). Limit behaviour of stochastic approximation processes. Statist. Decisions 6 109-128.
    • (1988) Statist. Decisions , vol.6 , pp. 109-128
    • Walk, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.