A Bayesian Stochastic Gradient Descent Method

This paper studies the sequential design to search for the minimizer of an unknown multi-dimensional convex function with observation error.We first propose an algorithmbased Kiefer-Wolfowitz method.We point out its discrepancy in choosing the optimal step length.Secondly,we propose a stochastic gradient decent method based on a Bayesian stochastic approximation method for root finding problem(Xu et al,2017).The proposed method features non-recursive adaptive learning and robustness comparing to some algorithm based method.Numerical examples are provided to illustrate the procedure.