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

Liu, Junyi & Cui, Ying & Pang, Jong-Shi. (2020). Solving Nonsmooth Nonconvex Compound Stochastic Programs with Applications to Risk Measure Minimization.

This paper studies a structured compound stochastic program involving multiple expectations coupled by nonconvex and nonsmooth functions. We present a successive convex-programming based sampling algorithm for solving this problem, establish its subsequential convergence, and discuss a probabilistic stopping rule 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.