# Wasserstein Distributionally Robust Optimization with Heterogeneous Data Sources

arXiv: https://arxiv.org/abs/2407.13582 · HTML: https://mlsanity.com/paper/2407.13582/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2024.

## Built on by (most cited first, 2 of 2)

- [Representation-Aware Distributionally Robust Optimization: A Knowledge Transfer Framework](https://mlsanity.com/paper/2509.09371/) (2025)
- [Robust Out-of-Distribution Stochastic Optimization](https://mlsanity.com/paper/2604.20147/) (2026)

## Abstract (arXiv)

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.