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

Resumo

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable con dence 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 con dence intervals on both the optimal values and optimal solutions. Numerical simulations show that our con dence intervals are much less conservative and are quicker to compute than previously obtained con dence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart. Our con dence intervals are also more reliable than asymptotic con dence intervals when the sample size is not much larger than the problem size.

Ficha do documento

Tipo

Artigo científico

Ano

2016

Instituição

EMAp - Escola de Matemática Aplicada

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Não informado

Identificador

oai:repositorio.fgv.br:10438/16241

Temas

Economia

Palavras-chave

Stochastic optimizationRisk measuresMultistep stochastic mirror descentRobust stochastic approximationEconomiaProcesso estocásticoRisco (Economia)Risco (Economia) - Medição - Modelos matemáticos