A randomized method for handling a difficult function in a convex optimization problem, motivated by probabilistic programming

Abstract

We propose a randomized gradient method for the handling of a convex function whose gradient computation is demanding. The method bears a resemblance to the stochastic approximation family. But in contrast to stochastic approximation, the present method builds a model problem. The approach requires that estimates of function values and gradients be provided at the iterates. We present a variance reduction Monte Carlo simulation procedure to provide such estimates in the case of certain probabilistic functions.