An empirical sensitivity analysis of the Kiefer-Wolfowitz algorithm and its variants

We investigate the mean-squared error (MSE) performance of the Kiefer-Wolfowitz (KW) stochastic approximation (SA) algorithm and two of its variants, namely the scaled-and-shifted KW (SSKW) in Broadie, Cicek, and Zeevi (2011) and Kesten's rule. We conduct a sensitivity analysis of KW with various tuning sequences and initial start values and implement the algorithms for two contrasting functions. From our numerical experiments, SSKW is less sensitive to initial start values under a set of pre-specified parameters, but KW and Kesten's rule outperform SSKW if they begin with well-tuned parameter values. We also investigate the tightness of an MSE bound for quadratic functions, a relevant issue for determining how long to run an SA algorithm. Our numerical experiments indicate the MSE bound for quadratic functions for the KW algorithm is sensitive to the noise level.