Distributionally Robust Convex Optimization

By Wolfram Wiesemann, D. Kühn, Melvyn Sim. Operational Research, 2014

1,025 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/01c41a647cc44f372903be729848ea6d56342773

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Wasserstein Distributional Robustness and Regularization in Statistical Learning (2017, background): “…of the statistical distance include φ -divergences (Ben-Tal et al. 2013, Jiang and Guan 2015, Bayraksan and Love 2015, Wang et al. 2016), Prokhorov metric (Erdo˘gan and Iyengar 2006), and Wasserstein distances (Wozabal 2014, Blanchet and Murthy 2016, Gao and Kleywegt 2016, Esfahani and Kuhn 2017).”
Robust SAA (2014, background): “In [43], the authors characterized the computational tractability of (3) for a wide range of DUSs F by connecting tractability to the geometry of F .”
Distributionally Robust Optimization: A Review (2019, methodology): “[318] propose a framework for modeling the ambiguity set of probability distributions as follows:”
Recent advances in robust optimization: An overview (2014, background): “Finally, Wiesemann et al. (2013b) propose a unifying framework for modeling and solving distributionally robust optimization problems based on standardized ambiguity sets that encompass many ambiguity sets from the recent literature as special cases.”
Outlier detection using distributionally robust optimization under the Wasserstein metric (2017, methodology): “eﬁned. One is through a moment ambiguity set, which contains all distributions that satisfy certain moment constraints (see Popescu, 2007; Delage and Ye, 2010; Goh and Sim, 2010; Zymler et al., 2013; Wiesemann et al., 2014). In many cases it leads to a tractable DRO problem but has been criticized f”
Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization (2016, background): “A non-exhaustive list includes moment and deviation-type constraints (Delage and Ye (2010), Goh and Sim (2010), Wiesemann et al. (2014)), Wasserstein balls (Esfahani and Kuhn (2015), Gao and Kleywegt (2016)), φ -divergence balls (Ben-Tal et al. (2013)), likelihood-based (Wang et al. (2015)) and…”
Regularization via Mass Transportation (2017, result): “…expected loss, where the worst case is taken with respect to all distributions in an ambiguity set, that is, a family of distributions consistent with the given prior information on the uncertainty, see, e.g. , Delage and Ye [15], Goh and Sim [20], Wiesemann et al. [41] and the references therein.”
Data-driven Affinely Adjustable Distributionally Robust Unit Commitment (2018, background): “The main results are stated in Theorem 1 inspired by [31].”
Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations (2015, background): “Specifically, there is growing evidence that distributionally robust models with moment ambiguity sets are more tractable than the corresponding stochastic models because the intractable high-dimensional integrals in the objective function are replaced with tractable (generalized) moment problems [1”
Distributionally Robust Logistic Regression (2015, methodology): “We validate our theoretical out-of-sample guarantees through simulated and empirical experiments.”
Adaptive Distributionally Robust Optimization (2019, background): “In terms of tractable formulations for a wide variety of single stage convex optimization problems, Wiesemann et al. (2014) propose a broad class of ambiguity sets where the family of probability distributions are characterized by conic representable expectation constraints and nested conic…”
Data-driven robust optimization (2013, background): “, [28,50] for recent work), to the best of our knowledge Ben-Tal et al.”
Robust sample average approximation (2014, background): “In [56], the authors characterized the computational tractability of (3) for a wide range of DUSs F by connecting tractability to the geometry of F .”
Quantifying Distributional Model Risk via Optimal Transport (2016, neutral): “There has been a broad range of ambiguity sets P that has been considered: For examples, refer Delage and Ye (2010); Goh and Sim (2010); Wiesemann et al. (2014) for moment-based uncertainty sets, Hansen and Sargent (2001); Iyengar (2005); Nilim and El Ghaoui (2005); Lim and Shanthikumar (2007);…”
Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming (2019, methodology): “In addition to generalized moment bounds [138], structural properties of distributions, such as symmetry, unimodality, multimodality and independence, were further integrated into distributionally robust chance constrained programs leveraging a Choquet representation [115].”
Regret in the Newsvendor Model with Demand and Yield Randomness (2021, background): “One popular choice is the moment-based ambiguity sets that are mainly concerned with (generalized) moments (see e.g., Chen et al. 2019, Delage and Ye 2010, El Ghaoui et al. 2003, Goh and Sim 2010, Li et al. 2019, Wiesemann et al. 2014, Xie and Ahmed 2018).”
Multi-stage distributionally robust optimization with risk aversion (2021, methodology): “[22] and [23] considered consider distributionally robust two-stage stochastic convex programming problems with ambiguity sets proposed by [50], and converted this class of problems to a conic optimization problems.”