I have just started learning stochastic approximation methods, so the question I'm going to ask may be a trivial one in this field, but I need to know this seriousely.
I know, that if $g(x,\xi)$ is a function of $x$, where $g(\cdot)$ is known, but $\xi$ is a random variable with some conditional distribution function $H(\cdot|x)$, then to solve for the zero of the function $\mathbb{E}[g(x,\xi)]$, we can use Robbins-Monro algorithm, and to find the maxima of $\mathbb{E}[g(x,\xi)]$, one can use the Keifer-Wolfowitz Algorithm. But, if I have a function of the kind $g(x,\xi_0)\ne \mathbb{E}[g(x,\xi)]$, where $\xi_0$ is not known to me but I can only get an estimate $\xi$ of $\xi_0$, and I want to find the zero of $g(x,\xi_0)$, then, is there any way I can use stochastic approximation? Thanks in advance.