Distributionally robust conditional quantile prediction with Wasserstein ball

A new data-driven distributionally robust framework was proposed for conditional quantile prediction. We extended the framework to accommodate general p -Wasserstein distances to enhance the robustness of the optimization problem and investigated quantile prediction using observed feature information. We employed a regression-then-robustify approach to obtain a robust data-driven solution to the quantile prediction problem and established finite-sample performance guarantees for this solution. We also reported the numerical performance of the proposed distributionally robust optimization (DRO) method through comparisons with other classical models.