Distributionally Robust Prescriptive Analytics with Wasserstein Distance

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...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Wang, Tianyu, Chen, Ningyuan, Wang, Chun
Format: Article
Language:English
Subjects:
Decision analysis
Decision making
Empirical analysis
Optimization
Parameter uncertainty
Robustness
Online Access:Get full text
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Summary: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.
ISSN:2331-8422