An adaptive multidimensional version of the Kiefer-Wolfowitz stochastic approximation algorithm

We extend the scaled-and-shifted Kiefer-Wolfowitz (SSKW) algorithm developed by Broadie, Cicek, and Zeevi (2009) to multiple dimensions. The salient feature of this algorithm is that it makes adjustments of the tuning parameters that adapt to the underlying problem characteristics. We compare the performance of this algorithm to the traditional Kiefer-Wolfowitz (KW) one and observe significant improvement in the finite-time performance on some stylized test functions and a multidimensional newsvendor problem.