# Data-driven Optimal Cost Selection for Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/1705.07152 · HTML: https://mlsanity.com/paper/1705.07152/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2017.

## Built on by (most cited first, 15 of 15)

- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Towards a Theoretical Framework of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.04496/) (2021)
- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Distributionally Robust Semi-Supervised Learning Over Graphs](https://mlsanity.com/paper/2110.10582/) (2021)
- [Geometry-Calibrated DRO: Combating Over-Pessimism with Free Energy Implications](https://mlsanity.com/paper/2311.05054/) (2023)
- [DRO: A Python Library for Distributionally Robust Optimization in Machine Learning](https://mlsanity.com/paper/2505.23565/) (2025)
- [Human Imperceptible Attacks and Applications to Improve Fairness](https://mlsanity.com/paper/2111.15603/) (2021)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [LLM Embeddings Improve Test-time Adaptation to Tabular Y|X-Shifts](https://mlsanity.com/paper/2410.07395/) (2024)
- [Dr. FERMI: A Stochastic Distributionally Robust Fair Empirical Risk Minimization Framework](https://mlsanity.com/paper/2309.11682/) (2023)
- [Robust, Deep, and Reinforcement Learning for Management of Communication and Power Networks](https://mlsanity.com/paper/2202.05395/) (2022)
- [Mixed-feature Logistic Regression Robust to Distribution Shifts](https://mlsanity.com/paper/2503.12012/) (2025)
- [Data Heterogeneity Modeling for Trustworthy Machine Learning](https://mlsanity.com/paper/2506.00969/) (2025)
- [Data Curation Matters: Model Collapse and Spurious Shift Performance Prediction from Training on Uncurated Text Embeddings](https://mlsanity.com/paper/2506.17989/) (2025)

## Abstract (arXiv)

Recently, (Blanchet, Kang, and Murhy 2016, and Blanchet, and Kang 2017) showed that several machine learning algorithms, such as square-root Lasso, Support Vector Machines, and regularized logistic regression, among many others, can be represented exactly as distributionally robust optimization (DRO) problems. The distributional uncertainty is defined as a neighborhood centered at the empirical distribution. We propose a methodology which learns such neighborhood in a natural data-driven way. We show rigorously that our framework encompasses adaptive regularization as a particular case. Moreover, we demonstrate empirically that our proposed methodology is able to improve upon a wide range of popular machine learning estimators.