  In this paper, we aim to solve Bayesian Risk Optimization (BRO), which is a
recently proposed framework that formulates simulation optimization under input
uncertainty. In order to efficiently solve the BRO problem, we derive nested
stochastic gradient estimators and propose corresponding stochastic
approximation algorithms. We show that our gradient estimators are
asymptotically unbiased and consistent, and that the algorithms converge
asymptotically. We demonstrate the empirical performance of the algorithms on a
two-sided market model. Our estimators are of independent interest in extending
the literature of stochastic gradient estimation to the case of nested risk
functions.
