Decomposition Algorithm for Distributionally Robust Optimization using Wasserstein Metric

TL;DR

This paper introduces a decomposition algorithm for distributionally robust optimization problems using the Wasserstein metric, reformulating them as semi-infinite programs and providing solution methods with demonstrated effectiveness.

Contribution

It presents a novel reformulation of Wasserstein-based DRO problems as semi-infinite programs and develops specific algorithms for nonlinear and convex cases.

Findings

The algorithms require 20-50 oracle calls for high precision.

The robust logistic regression model improves prediction accuracy.

Solutions have smaller standard errors in predictions.

Abstract

We study distributionally robust optimization (DRO) problems where the ambiguity set is defined using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-infinite 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.