论文标题
解决非平滑非凸复合随机程序，并使用应用程序最小化的风险衡量
Solving Nonsmooth Nonconvex Compound Stochastic Programs with Applications to Risk Measure Minimization
论文作者
论文摘要
本文研究了一个结构化的化合物随机程序（SP），涉及由非凸和非平滑函数结合的多个期望。我们提出了连续的基于凸编程的采样算法，并建立了其后续收敛。我们描述了几类化合物SP的限制点的平稳性属性。我们进一步讨论了基于算法的可计算错误限制的概率停止规则。我们提出了几种风险衡量最小化问题，可以作为这种复合随机计划提出。这些包括基于优化确定性的超出性和缓冲概率（BPOE）的广义偏差优化问题（BPOE），强大的BPOE优化问题以及使用BPOE风险度量的成本敏感误差标准的多类分类问题。
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 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.
