| [1] Robbins H, Siegmund D. A stochastic approximation method[J]. Ann Math Statist, 1951,22:400-407.[2] Kiefer E, Wolfovitz J. Stochastic estimation of the maximum of a regression function[J]. Ann Math Statist, 1952,23:462-466.[3] Kornfelev A P, Stochastic recurrent procedures[M]. Nauka, 1981 (in Russian).[4] Kushner H J, Clark D S, Stochastic approximation methods for constrained and unconstrained systems[M].Springer, New York, 1978.[5] Nemirovski A, Juditsky A, Lan G,et al. Robust stochastic approximation approach to stochastic programming[J]. SIAM J Optim, 2009,19:1 574-1 609.[6] Stein M L, Chen J, Anitescu M. Stochastic approximation of score functions for Gaussian processes[J]. Ann Appl Stat, 2013,7:1 162-1 191.[7] Benaim M, Faure M. Stochastic approximation, cooperative dynamics and supermodular games[J]. Ann Appl Probab, 2012,22:2 133-2 164.[8] Koshal J, Nedic A, Shanbhag U V. Regularized iterative stochastic approximation methods for stochastic variational inequality problems[J]. IEEE Trans Automat Control, 2013, 58:594-609.[9] Polyak B T. New stochastic approximation type procedures[J]. Avtomat Telemekh, 1990,N7:98-107(in Russian).[10] Ruppert D. Efficient estimators from a slowly convergent Robbins-Monro process[R]. Tech Report No. 781, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY, 1988.[11] Polyak B T, Juditsky A B. Acceleration of stochastic approximation by averaging[J]. SIAM J Control and optimization, 1992,30:838-855.[12] 陈翰馥, 朱允民.随机逼近[M]. 上海:上海科学技术出版社, 1996.[13] 陈翰馥, 扩展截尾的随机逼近算法[J].系统科学与数学, 2012, 12:1 472-1 487[14] Liptzer R S, Shiryaev A N. Martingale theory[M]. Nauka, Moscow,1986(in Russian). |
