  We analyze the tail behavior of solutions to sample average approximations
(SAAs) of stochastic programs posed in Hilbert spaces. We require that the
integrand be strongly convex with the same convexity parameter for each
realization. Combined with a standard condition from the literature on
stochastic programming, we establish non-asymptotic exponential tail bounds for
the distance between the SAA solutions and the stochastic program's solution,
without assuming compactness of the feasible set. Our assumptions are verified
on a class of infinite-dimensional optimization problems governed by
affine-linear partial differential equations with random inputs.
