# Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk

arXiv: https://arxiv.org/abs/2604.18546 · HTML: https://mlsanity.com/paper/2604.18546/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 16 of 16)

- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Fairness risk measures](https://mlsanity.com/paper/1901.08665/) (2019)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Statistical Learning with Conditional Value at Risk](https://mlsanity.com/paper/2002.05826/) (2020)
- [Wasserstein Distributionally Robust Kalman Filtering](https://mlsanity.com/paper/1809.08830/) (2018)
- [Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts](https://mlsanity.com/paper/2106.00322/) (2021)
- [Bridging Bayesian and Minimax Mean Square Error Estimation via Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/1911.03539/) (2019)
- [Mean-Covariance Robust Risk Measurement](https://mlsanity.com/paper/2112.09959/) (2021)
- [Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation](https://mlsanity.com/paper/2201.00508/) (2022)
- [Wasserstein Distributionally Robust Estimation in High Dimensions: Performance Analysis and Optimal Hyperparameter Tuning](https://mlsanity.com/paper/2206.13269/) (2022)
- [Toward a Scalable Upper Bound for a CVaR-LQ Problem](https://mlsanity.com/paper/2103.02136/) (2021)
- [On the Robustness of the Bayes and Wiener Estimators under Model Uncertainty](https://mlsanity.com/paper/1508.01904/) (2015)
- [A Distributionally Robust Approach to Regret Optimal Control using the Wasserstein Distance](https://mlsanity.com/paper/2304.06783/) (2023)

## Abstract (arXiv)

We propose a distributionally robust approach to risk-sensitive estimation of an unknown signal x from an observed signal y. The observation and unknown signal are modeled as random vectors whose joint probability distribution is unknown, but assumed to belong to a given type-2 Wasserstein ball of distributions, termed the ambiguity set. The performance of an estimator is measured according to the conditional value-at-risk (CVaR) of the squared estimation error. Within this framework, we study the problem of computing affine estimators that minimize the worst-case CVaR over all distributions in the given ambiguity set. As our main result, we show that, when the nominal distribution at the center of the Wasserstein ball is finitely supported, such estimators can be exactly computed by solving a tractable semidefinite program. We evaluate the proposed estimators on a wholesale electricity price forecasting task using real market data and show that they deliver lower out-of-sample CVaR of squared error compared to existing methods.