  We discretize a risk-neutral optimal control problem governed by a linear
elliptic partial differential equation with random inputs using a Monte Carlo
sample-based approximation and a finite element discretization, yielding finite
dimensional control problems. We establish an exponential tail bound for the
distance between the finite dimensional problems' solutions and the
risk-neutral problem's solution. The tail bound implies that solutions to the
risk-neutral optimal control problem can be reliably estimated with the
solutions to the finite dimensional control problems. Numerical simulations
illustrate our theoretical findings.
