Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems
Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems
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DOI：
10.1287/opre.1090.0741
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发表时间：
2010-05-01
影响因子：
2.7
通讯作者：
Ye, Yinyu
中科院分区：
文献类型：
--
作者：
Delage, Erick;Ye, Yinyu
随机规划可以有效地描述不确定环境下的许多决策问题。不幸的是，这样的程序通常需要计算来解决。此外，当随机参数的分布选择存在模糊性时，他们的解决方案可能会产生误导。在本文中，我们提出了一个模型，描述了两种分布形式（离散，高斯，指数等）的不确定性。矩（mean and covariance matrix）我们证明，对于广泛的成本函数的相关分布鲁棒（或最小最大）随机规划可以有效地解决。此外，通过推导一个新的置信区间的均值和协方差矩阵的随机向量，我们提供了概率参数使用我们的模型在很大程度上依赖于历史数据的问题。这些论点在投资组合选择的一个实际例子中得到了证实，在这个例子中，我们的框架导致了对金融资产每日回报率的“真实”分布的更好的执行政策。
Stochastic programming can effectively describe many decision-making problems in uncertain environments. Unfortunately, such programs are often computationally demanding to solve. In addition, their solution can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix). We demonstrate that for a wide range of cost functions the associated distributionally robust (or min-max) stochastic program can be solved efficiently. Furthermore, by deriving a new confidence region for the mean and the covariance matrix of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. These arguments are confirmed in a practical example of portfolio selection, where our framework leads to better-performing policies on the "true" distribution underlying the daily returns of financial assets.