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

arXiv 2604.18546 ↗First posted 20 Apr 2026cs.LG eess.SP math.OCcited by 0

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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.

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References · 16

  1. 2015Risk-Constrained Reinforcement Learning with Percentile Risk Criteriacited by 320
  2. 2019Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learningcited by 169
  3. 2015Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approachcited by 162
  4. 2015Distributionally Robust Logistic Regressioncited by 124
  5. 2019Fairness risk measurescited by 85
  6. 2017Regularization via Mass Transportationcited by 79
  7. 2020Statistical Learning with Conditional Value at Riskcited by 19
  8. 2018Wasserstein Distributionally Robust Kalman Filteringcited by 17
  9. 2021Sequential Domain Adaptation by Synthesizing Distributionally Robust Expertscited by 14
  10. 2019Bridging Bayesian and Minimax Mean Square Error Estimation via Wasserstein Distributionally Robust Optimizationcited by 11
  11. 2022Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computationcited by 10
  12. 2021Mean-Covariance Robust Risk Measurementcited by 9
4 more
  1. 2022Wasserstein Distributionally Robust Estimation in High Dimensions: Performance Analysis and Optimal Hyperparameter Tuningcited by 6
  2. 2021Toward a Scalable Upper Bound for a CVaR-LQ Problemcited by 4
  3. 2015On the Robustness of the Bayes and Wiener Estimators under Model Uncertaintycited by 3
  4. 2023A Distributionally Robust Approach to Regret Optimal Control using the Wasserstein Distancecited by 3

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