Wasserstein Distributionally Robust Optimization with Heterogeneous Data Sources

TL;DR

This paper develops a Wasserstein distributionally robust optimization framework that leverages multiple biased data sources, improving decision-making under uncertainty and providing computationally tractable solutions.

Contribution

It introduces a novel DRO approach using intersection of OT neighborhoods for multiple biased data sources, with theoretical guarantees and tractability results.

Findings

Out-of-sample performance improves with more data sources, regardless of bias magnitude.

The proposed DRO problem is computationally tractable under standard convexity assumptions.

The method effectively exploits biased data sources to enhance decision robustness.

Abstract

We study decision problems under uncertainty, where the decision-maker has access to $K$ data sources that carry {\em biased} information about the underlying risk factors. The biases are measured by the mismatch between the risk factor distribution and the $K$ data-generating distributions with respect to an optimal transport (OT) distance. In this situation the decision-maker can exploit the information contained in the biased samples by solving a distributionally robust optimization (DRO) problem, where the ambiguity set is defined as the intersection of $K$ OT neighborhoods, each of which is centered at the empirical distribution on the samples generated by a biased data source. We show that if the decision-maker has a prior belief about the biases, then the out-of-sample performance of the DRO solution can improve with $K$ -- irrespective of the magnitude of the biases. We also show that, under standard convexity assumptions, the proposed DRO problem is computationally tractable if either $K$ or the dimension of the risk factors is kept constant.