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

TL;DR

This paper introduces a distributionally robust risk-sensitive estimation method using Wasserstein ambiguity sets and CVaR, providing a tractable solution for affine estimators with real-world electricity forecasting applications.

Contribution

It develops a novel approach to risk-sensitive estimation under Wasserstein ambiguity, with a tractable semidefinite program for finitely supported distributions, and demonstrates improved performance in electricity price forecasting.

Findings

Exact affine estimators computed via semidefinite programming

Lower out-of-sample CVaR of squared error in electricity forecasting

Method outperforms existing approaches in robustness and risk sensitivity

Abstract

We propose a distributionally robust approach to risk-sensitive estimation of an unknown signal x from an observed signal y. The unknown signal and observation 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.