Decomposition algorithm for distributionally robust optimization using Wasserstein metric with an application to a class of regression models

Fengqiao Luo, Sanjay Mehrotra*

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We study distributionally robust optimization (DRO) problems where the ambiguity set is defined using the Wasserstein metric and can account for a bounded support. We show that this class of DRO problems can be reformulated as decomposable semi-infinite programs. We use a cutting-surface method to solve the reformulated problem for the general nonlinear model, assuming that we have a separation oracle. As examples, we consider the problems arising from the machine learning models where variables couple with data in a bilinear form in the loss function. We present a branch-and-bound algorithm to solve the separation problem for this case using an iterative piece-wise linear approximation scheme. We use a distributionally robust generalization of the logistic regression model to test our algorithm. We also show that it is possible to approximate the logistic-loss function with significantly less linear pieces than those needed for a general loss function to achieve a given accuracy when generating a cutting surface. 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 has better predicting power than classical logistic regression when the sample size is small.

Original languageEnglish (US)
Pages (from-to)20-35
Number of pages16
JournalEuropean Journal of Operational Research
Volume278
Issue number1
DOIs
StatePublished - Oct 1 2019

Keywords

  • Distributionally robust optimization
  • Logistic regression
  • Robustness and sensitivity analysis
  • Semi-infinite programming
  • Wasserstein metric

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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