# Sensitivity analysis of Wasserstein distributionally robust optimization problems

arXiv: https://arxiv.org/abs/2006.12022 · HTML: https://mlsanity.com/paper/2006.12022/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2020.

## Built on by (most cited first, 11 of 11)

- [Wasserstein distributional robustness of neural networks](https://mlsanity.com/paper/2306.09844/) (2023)
- [Robust Risk-Aware Option Hedging](https://mlsanity.com/paper/2303.15216/) (2023)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [Wasserstein Distributionally Robust Nonparametric Regression](https://mlsanity.com/paper/2505.07967/) (2025)
- [Wasserstein Distributionally Robust Regret Optimization](https://mlsanity.com/paper/2504.10796/) (2025)
- [Distributional Adversarial Attacks and Training in Deep Hedging](https://mlsanity.com/paper/2508.14757/) (2025)
- [Wasserstein distributional adversarial training for deep neural networks](https://mlsanity.com/paper/2502.09352/) (2025)
- [Uncertainty-Aware Strategies: A Model-Agnostic Framework for Robust Financial Optimization through Subsampling](https://mlsanity.com/paper/2506.07299/) (2025)
- [Concave Certificates: Geometric Framework for Distributionally Robust Risk and Complexity Analysis](https://mlsanity.com/paper/2601.01311/) (2026)
- [Policy Gradient Learning for Distributionally Robust Markov Decision Processes under Wasserstein Ambiguity](https://mlsanity.com/paper/2606.27610/) (2026)

## Abstract (arXiv)

We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for the first order correction to both the value function and the optimizer and further extend our results to optimization under linear constraints. We present applications to statistics, machine learning, mathematical finance and uncertainty quantification. In particular, we provide explicit first-order approximation for square-root LASSO regression coefficients and deduce coefficient shrinkage compared to the ordinary least squares regression. We consider robustness of call option pricing and deduce a new Black-Scholes sensitivity, a non-parametric version of the so-called Vega. We also compute sensitivities of optimized certainty equivalents in finance and propose measures to quantify robustness of neural networks to adversarial examples.