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Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations
It is demonstrated that 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.
Distributionally Robust Convex Optimization
A unifying framework for modeling and solving distributionally robust optimization problems and introduces standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold.
Robust Markov Decision Processes
This work considers robust MDPs that offer probabilistic guarantees in view of the unknown parameters to counter the detrimental effects of estimation errors and determines a policy that attains the highest worst-case performance over this confidence region.
Distributionally robust joint chance constraints with second-order moment information
It is proved that this approximation is exact for robust individual chance constraints with concave or (not necessarily concave) quadratic constraint functions, and it is demonstrated that the Worst-Case CVaR can be computed efficiently for these classes of constraint functions.
Distributionally Robust Logistic Regression
- Soroosh Shafieezadeh-Abadeh, Peyman Mohajerin Esfahani, D. Kuhn
- Computer Science, MathematicsNIPS
- 30 September 2015
This paper uses the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples, and proposes a distributionally robust logistic regression model that minimizes a worst-case expected logloss function.
Regularization via Mass Transportation
- Soroosh Shafieezadeh-Abadeh, D. Kuhn, Peyman Mohajerin Esfahani
- Computer ScienceJ. Mach. Learn. Res.
- 27 October 2017
This paper introduces new regularization techniques using ideas from distributionally robust optimization, and gives new probabilistic interpretations to existing techniques to minimize the worst-case expected loss, where the worst case is taken over the ball of all distributions that have a bounded transportation distance from the empirical distribution.
Generalized Gauss inequalities via semidefinite programming
This paper obtains a less pessimistic Gauss-type bound by imposing the additional requirement that the random vector’s distribution must be unimodal, and proves that this generalized Gauss bound still admits an exact and tractable semidefinite representation.
A scenario approach for estimating the suboptimality of linear decision rules in two-stage robust optimization
- Michael J. Hadjiyiannis, P. Goulart, D. Kuhn
- Computer ScienceIEEE Conference on Decision and Control and…
- 1 December 2011
This paper investigates families of tractable lower bounding approximations, which serve to estimate the degree of suboptimality of the best LDR, and proposes an efficient procedure to construct suboptimal lower bounds.
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning
- D. Kuhn, Peyman Mohajerin Esfahani, Viet Anh Nguyen, Soroosh Shafieezadeh-Abadeh
- Computer ScienceOperations Research & Management Science in the…
- 23 August 2019
This tutorial argues that Wasserstein distributionally robust optimization has interesting ramifications for statistical learning and motivates new approaches for fundamental learning tasks such as classification, regression, maximum likelihood estimation or minimum mean square error estimation, among others.
Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls
It is shown that two-stage robust and distributionally robust linear programs can often be reformulated exactly as conic programs that scale polynomially with the problem dimensions.