Distributionally Robust Prescriptive Analytics with Wasserstein Distance
This work addresses decision-making under uncertainty for practitioners in fields like operations research and finance, though it is incremental as it builds on existing distributionally robust optimization methods.
The paper tackles the problem of making decisions under uncertainty in prescriptive analytics by proposing a distributionally robust approach using Wasserstein ambiguity sets, with results showing strong performance in synthetic and empirical experiments like the newsvendor problem and portfolio optimization.
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.