Adaptive algorithms and stochastic approximations
Adaptive algorithms and stochastic approximations
Acceleration of stochastic approximation by averaging
SIAM Journal on Control and Optimization
A scaled stochastic approximation algorithm
Management Science
Weighted Means in Stochastic Approximation of Minima
SIAM Journal on Control and Optimization
Robust Stochastic Approximation Approach to Stochastic Programming
SIAM Journal on Optimization
Dynamic Pricing Under a General Parametric Choice Model
Operations Research
Averaging and derivative estimation within stochastic approximation algorithms
Proceedings of the Winter Simulation Conference
An introspective on the retrospective-approximation paradigm
Proceedings of the Winter Simulation Conference
A Bayesian approach to stochastic root finding
Proceedings of the Winter Simulation Conference
Proceedings of the Winter Simulation Conference
Multidimensional stochastic approximation: Adaptive algorithms and applications
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on simulation in complex service systems
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We consider the Kiefer-Wolfowitz (KW) stochastic approximation algorithm and derive general upper bounds on its mean-squared error. The bounds are established using an elementary induction argument and phrased directly in the terms of tuning sequences of the algorithm. From this we deduce the nonnecessity of one of the main assumptions imposed on the tuning sequences by Kiefer and Wolfowitz [Kiefer, J., J. Wolfowitz. 1952. Stochastic estimation of the maximum of a regression function. Ann. Math. Statist.23(3) 462--466] and essentially all subsequent literature. The optimal choice of sequences is derived for various cases of interest, and an adaptive version of the KW algorithm, scaled-and-shifted KW (or SSKW), is proposed with the aim of improving its finite-time behavior. The key idea is to dynamically scale and shift the tuning sequences to better match them with characteristics of the unknown function and noise level, and thus improve algorithm performance. Numerical results are provided that illustrate that the proposed algorithm retains the convergence properties of the original KW algorithm while dramatically improving its performance in some cases.