论文标题
在Wasserstein歧义集中的分布稳健风险和机会约束优化的一致性
Consistency of Distributionally Robust Risk- and Chance-Constrained Optimization under Wasserstein Ambiguity Sets
论文作者
论文摘要
我们研究随机和风险限制的随机优化问题，在后者中，风险是根据风险的条件价值（CVAR）量化的。我们考虑了这些问题的分布稳健版本，其中需要约束，以通过Wasserstein距离从观察到的不确定性实现构建的分布家族。我们的主要结果表明，如果样本是独立于潜在的分布绘制的，并且问题满足了合适的技术假设，则随着样本量的增加，这些问题的最佳价值和优化者会融合到原始问题的各自数量。
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where the constraints are required to hold for a family of distributions constructed from the observed realizations of the uncertainty via the Wasserstein distance. Our main results establish that if the samples are drawn independently from an underlying distribution and the problems satisfy suitable technical assumptions, then the optimal value and optimizers of the distributionally robust versions of these problems converge to the respective quantities of the original problems, as the sample size increases.
