  We consider the solution of a stochastic convex optimization problem
$\mathbb{E}[f(x;\theta^*,\xi)]$ over a closed and convex set $X$ in a regime
where $\theta^*$ is unavailable and $\xi$ is a suitably defined random
variable. Instead, $\theta^*$ may be obtained through the solution of a
learning problem that requires minimizing a metric $\mathbb{E}[g(\theta;\eta)]$
in $\theta$ over a closed and convex set $\Theta$. Traditional approaches have
been either sequential or direct variational approaches. In the case of the
former, this entails the following steps: (i) a solution to the learning
problem, namely $\theta^*$, is obtained; and (ii) a solution is obtained to the
associated computational problem which is parametrized by $\theta^*$. Such
avenues prove difficult to adopt particularly since the learning process has to
be terminated finitely and consequently, in large-scale instances, sequential
approaches may often be corrupted by error. On the other hand, a variational
approach requires that the problem may be recast as a possibly non-monotone
stochastic variational inequality problem in the $(x,\theta)$ space; but there
are no known first-order stochastic approximation schemes are currently
available for the solution of this problem. To resolve the absence of
convergent efficient schemes, we present a coupled stochastic approximation
scheme which simultaneously solves both the computational and the learning
problems. The obtained schemes are shown to be equipped with almost sure
convergence properties in regimes when the function $f$ is either strongly
convex as well as merely convex.
