  The goal of this paper is to solve a class of stochastic optimal control
problems numerically, in which the state process is governed by an It\^o type
stochastic differential equation with control process entering both in the
drift and the diffusion, and is observed partially. The optimal control of
feedback form is determined based on the available observational data. We call
this type of control problems the data driven feedback control. The
computational framework that we introduce to solve such type of problems aims
to find the best estimate for the optimal control as a conditional expectation
given the observational information. To make our method feasible in providing
timely feedback to the controlled system from data, we develop an efficient
stochastic optimization algorithm to implement our computational framework.
