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Decomposition Algorithms for Distributionally Robust Optimization using Wasserstein Metric

Fengqiao Luo(fengqiaoluo2014***at***u.northwestern.edu)
Sanjay Mehrotra(mehrotra***at***northwestern.edu)

Abstract: We study distributionally robust optimization (DRO) problems where the ambiguity set is de ned using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-in nite programs. We give an exchange method to solve the reformulated problem for the general nonlinear model, and a central cutting-surface method for the convex case, assuming that we have a separation oracle. We used a distributionally robust generalization of the logistic regression model to test our algorithm. Numerical experiments on the distributionally robust logistic regression models show that the number of oracle calls are typically 20~50 to achieve 5-digit precision. The solution found by the model is generally better in its ability to predict with a smaller standard error.

Keywords: distributionally robust optimization, Wasserstein metric, semi-infinite programming, cutting-surface algorithms, exchange method

Category 1: Robust Optimization

Category 2: Infinite Dimensional Optimization (Semi-infinite Programming )

Category 3: Applications -- Science and Engineering (Data-Mining )


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Entry Submitted: 04/06/2017
Entry Accepted: 04/06/2017
Entry Last Modified: 04/06/2017

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