Distributionally Robust Prescriptive Analytics with Wasserstein Distance

TL;DR

This paper introduces a distributionally robust prescriptive analytics method using Wasserstein distance, leveraging kernel estimators to improve decision-making under uncertainty with theoretical guarantees and practical effectiveness.

Contribution

It develops a novel Wasserstein-based distributionally robust approach for prescriptive analytics that uses kernel estimators for conditional distributions, with proven convergence and out-of-sample guarantees.

Findings

Strong empirical performance in newsvendor and portfolio problems

Theoretical convergence of the nominal distribution to the true conditional

Out-of-sample guarantees and computational tractability

Abstract

In prescriptive analytics, the decision-maker observes historical samples of $(X, Y)$, where $Y$ is the uncertain problem parameter and $X$ is the concurrent covariate, without knowing the joint distribution. Given an additional covariate observation $x$, the goal is to choose a decision $z$ conditional on this observation to minimize the cost $\mathbb{E}[c(z,Y)|X=x]$. This paper proposes a new distributionally robust approach under Wasserstein ambiguity sets, in which the nominal distribution of $Y|X=x$ is constructed based on the Nadaraya-Watson kernel estimator concerning the historical data. We show that the nominal distribution converges to the actual conditional distribution under the Wasserstein distance. We establish the out-of-sample guarantees and the computational tractability of the framework. Through synthetic and empirical experiments about the newsvendor problem and portfolio optimization, we demonstrate the strong performance and practical value of the proposed framework.