Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on...

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Vydáno v:Mathematical programming Ročník 171; číslo 1-2; s. 115 - 166
Hlavní autoři: Mohajerin Esfahani, Peyman, Kuhn, Daniel
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2018
Springer Nature B.V
Témata:
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Economic models
Full Length Paper
Global optimization
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Monte Carlo simulation
Nonlinear programming
Numerical Analysis
Optimization techniques
Parameter uncertainty
Theoretical
Training
90C25 Convex programming
90C47 Minimax problems
90C15 Stochastic programming
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí:We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worst-case distribution within this Wasserstein ball. The state-of-the-art methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques, which quickly become computationally excruciating. In this paper we demonstrate that, under mild assumptions, the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs—in many interesting cases even as tractable linear programs. Leveraging recent measure concentration results, we also show that their solutions enjoy powerful finite-sample performance guarantees. Our theoretical results are exemplified in mean-risk portfolio optimization as well as uncertainty quantification.
Bibliografie:ObjectType-Article-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-017-1172-1