Low-rank distributionally robust optimization

Abstract: In many data-driven decision problems a few common factors drive most of the uncertainty. Wasserstein distributionally robust optimization (DRO) protects decisions against errors in the empirical distribution. However, it spreads that protection in every direction, including directions where the data shows almost no variation, which can make decisions needlessly conservative. In this talk, I present a low-rank Wasserstein DRO framework. It projects the observations onto a low-dimensional subspace, chosen from domain knowledge or estimated from data, and allows the distribution to be perturbed only within that subspace. Choosing the subspace dimension gives a bias–variance tradeoff. A smaller subspace discards more of the variation in the data, while a larger one restores protection in directions that matter little. We characterize when this restriction leads to decisions that full-space DRO cannot reach at any choice of radius. Experiments in portfolio, assortment and facility location problems show that the low-rank model can improve performance.