Solving Nonsmooth and Nonconvex Compound Stochastic Programs with Applications to Risk Measure Minimization
提出一种基于逐次凸规划的采样算法，求解含多个期望的非凸非光滑复合随机规划问题，并证明其子序列收敛性；该框架可应用于多种风险测度最小化问题，如基于缓冲超限概率的优化和分类问题。
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 stationary 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 the 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.