General multilevel adaptations for stochastic approximation algorithms of Robbins–Monro and Polyak–Ruppert type

[1]  Peter W. Glynn,et al.  Unbiased Estimation with Square Root Convergence for SDE Models , 2015, Oper. Res..

[2]  N. Frikha.  Multi-level stochastic approximation algorithms , 2013, 1310.2052.

[3]  Mariane Pelletier,et al.  A Generalization of the Averaging Procedure: The Use of Two-Time-Scale Algorithms , 2011, SIAM J. Control. Optim..

[4]  Don McLeish,et al.  A general method for debiasing a Monte Carlo estimator , 2010, Monte Carlo Methods Appl..

[5]  Michael B. Giles,et al.  Multilevel Monte Carlo Path Simulation , 2008, Oper. Res..

[6]  Vijay R. Konda,et al.  Convergence rate of linear two-time-scale stochastic approximation , 2004, math/0405287.

[7]  H. Kushner,et al.  Stochastic Approximation and Recursive Algorithms and Applications , 2003 .

[8]  T. Lai.  Stochastic approximation: invited paper , 2003 .

[9]  Stefan Heinrich,et al.  Multilevel Monte Carlo Methods , 2001, LSSC.

[10]  M. Pelletier.  On the almost sure asymptotic behaviour of stochastic algorithms , 1998 .

[11]  M. Pelletier.  Weak convergence rates for stochastic approximation with application to multiple targets and simulated annealing , 1998 .

[12]  J. Dippon,et al.  Weighted Means in Stochastic Approximation of Minima , 1997 .

[13]  Alexander Novikov,et al.  Some results about averaging in stochastic approximation , 1995 .

[14]  D. Nualart.  The Malliavin Calculus and Related Topics , 1995 .

[15]  H. Kushner,et al.  Stochastic approximation with averaging of the iterates: Optimal asymptotic rate of convergence for , 1993 .

[16]  Boris Polyak,et al.  Acceleration of stochastic approximation by averaging , 1992 .

[17]  G. Pflug,et al.  Stochastic approximation and optimization of random systems , 1992 .

[18]  B. K. Ghosh,et al.  Handbook of sequential analysis , 1991 .

[19]  Pierre Priouret,et al.  Adaptive Algorithms and Stochastic Approximations , 1990, Applications of Mathematics.

[20]  D. Ruppert.  Almost Sure Approximations to the Robbins-Monro and Kiefer-Wolfowitz Processes with Dependent Noise , 1982 .

[21]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[22]  H Robbins,et al.  Limit theorems for weighted sums and stochastic approximation processes. , 1978, Proceedings of the National Academy of Sciences of the United States of America.

[23]  T. P. Krasulina,et al.  On the Law of the Iterated Logarithm in Stochastic Approximation Processes , 1975 .

[24]  V. Fabian.  On Asymptotic Normality in Stochastic Approximation , 1968 .

[25]  J. Sacks.  Asymptotic Distribution of Stochastic Approximation Procedures , 1958 .

[26]  J. Kiefer,et al.  Stochastic Estimation of the Maximum of a Regression Function , 1952 .

[27]  H. Robbins.  A Stochastic Approximation Method , 1951 .

[28]  Tze Leung Lai,et al.  Stochastic approximation , 2018 .

[29]  Abdelkader Mokkadem,et al.  On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density , 2008 .

[30]  David Nualart Rodón,et al.  The Malliavin Calculus and Related Topics , 2006 .

[31]  E. Zeidler,et al.  Mathematik und Informatik , 1995 .

[32]  F. Downton.  Stochastic Approximation , 1969, Nature.