Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems

Operations Research - Tập 58 Số 3 - Trang 595-612 - 2010
Erick Delage1, Yinyu Ye2
1Department of Management Sciences, HEC Montréal, Montreal, Quebec H3T 2A7, Canada
2Department of Management Science and Engineering, Stanford University, Stanford, California 94305

Tóm tắt

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.

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Operations Research

Tập 58 Số 3

595-612

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