  This paper studies a structured compound stochastic program (SP) involving
multiple expectations coupled by nonconvex and nonsmooth functions. We present
a successive convex-programming based sampling algorithm and establish its
subsequential convergence. We describe stationarity properties of the limit
points for several classes of the compound SP. We further discuss probabilistic
stopping rules based on the computable error-bound for the algorithm. We
present several risk measure minimization problems that can be formulated as
such a compound stochastic program; these include generalized deviation
optimization problems based on optimized certainty equivalent and buffered
probability of exceedance (bPOE), a distributionally robust bPOE optimization
problem, and a multiclass classification problem employing the cost-sensitive
error criteria with bPOE risk measure.
