  In applications of imprecise probability, analysts must compute lower (or
upper) expectations, defined as the infimum of an expectation over a set of
parameter values. Monte Carlo methods consistently approximate expectations at
fixed parameter values, but can be costly to implement in grid search to locate
minima over large subsets of the parameter space. We investigate the use of
stochastic iterative root-finding methods for efficiently computing lower
expectations. In two examples we illustrate the use of various stochastic
approximation methods, and demonstrate their superior performance in comparison
to grid search.
