# Wasserstein Distributionally Robust Estimation in High Dimensions: Performance Analysis and Optimal Hyperparameter Tuning

arXiv: https://arxiv.org/abs/2206.13269 · HTML: https://mlsanity.com/paper/2206.13269/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2022.

## Built on by (most cited first, 6 of 6)

- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [A Novel Gaussian Min-Max Theorem and its Applications](https://mlsanity.com/paper/2402.07356/) (2024)
- [Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergences](https://mlsanity.com/paper/2603.27871/) (2026)
- [Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk](https://mlsanity.com/paper/2604.18546/) (2026)
- [Distributionally robust linear regression through the lens of adversarial training](https://mlsanity.com/paper/2609.39449/) (2026)

## Abstract (arXiv)

Distributionally robust optimization (DRO) has become a powerful framework for estimation under uncertainty, offering strong out-of-sample performance and principled regularization. In this paper, we propose a DRO-based method for linear regression and address a central question: how to optimally choose the robustness radius, which controls the trade-off between robustness and accuracy. Focusing on high-dimensional settings where the dimension and the number of samples are both large and comparable in size, we employ tools from high-dimensional asymptotic statistics to precisely characterize the estimation error of the resulting estimator. Remarkably, this error can be recovered by solving a simple convex-concave optimization problem involving only four scalar variables. This characterization enables efficient selection of the radius that minimizes the estimation error. In doing so, it achieves the same effect as cross-validation, but at a fraction of the computational cost. Numerical experiments confirm that our theoretical predictions closely match empirical performance and that the optimal radius selected through our method aligns with that chosen by cross-validation, highlighting both the accuracy and the practical benefits of our approach.