Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

• 成果类型: Article
• 署名作者: Guigues, Vincent
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1060-0
• 发表日期: 2017
• 页码: 169-212
• 关键词: statistical estimators; complete recourse; solution quality; approximation; optimization

摘要

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic Mirror Descent algorithm and obtain confidence intervals on both the optimal values and optimal solutions. Numerical simulations show that our confidence intervals are much less conservative and are quicker to compute than previously obtained confidence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart.