  We consider the problem of estimating a probability distribution that
maximizes the entropy while satisfying a finite number of moment constraints,
possibly corrupted by noise. Based on duality of convex programming, we present
a novel approximation scheme using a smoothed fast gradient method that is
equipped with explicit bounds on the approximation error. We further
demonstrate how the presented scheme can be used for approximating the chemical
master equation through the zero-information moment closure method, and for an
approximate dynamic programming approach in the context of constrained Markov
decision processes with uncountable state and action spaces.
