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This paper studies a structured compound stochastic program (SP) involvingmultiple expectations coupled by nonconvex and nonsmooth functions. We presenta successive convex-programming based sampling algorithm and establish itssubsequential convergence. We describe stationarity properties of the limitpoints for several classes of the compound SP. We further discuss probabilisticstopping rules based on the computable error-bound for the algorithm. Wepresent several risk measure minimization problems that can be formulated assuch a compound stochastic program; these include generalized deviationoptimization problems based on optimized certainty equivalent and bufferedprobability of exceedance (bPOE), a distributionally robust bPOE optimizationproblem, and a multiclass classification problem employing the cost-sensitiveerror criteria with bPOE risk measure.

Solving Nonsmooth Nonconvex Compound Stochastic Programs with Applications to Risk Measure Minimization