Robust SAA

By Dimitris J. Bertsimas, Vishal Gupta, Nathan Kallus. 2014

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Citations in the corpus

Variance-based Regularization with Convex Objectives (2016, methodology): “In this paper, we develop an approach based on Owen’s empirical likelihood [19] and ideas from distributionally robust optimization [4, 5, 10] that—whenever the loss ` is convex—provides a tractable convex formulation closely approximating the penalized risk (3).”
Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations (2015, background): “6(i) requires h(x, ξ) to be upper semicontinuous in ξ , which is a necessary condition in our setting (see Example 1) that is absent in [7].”
Smart "Predict, then Optimize" (2017, background): “…from data include operational statistics (Liyanage and Shanthikumar (2005), Chu et al. (2008)), sample average approximation (Kleywegt et al. (2002), Schütz et al. (2009), Bertsimas et al. (2014)), and robust optimization (Bertsimas and Thiele (2006), Bertsimas et al. (2013), Wang et al. (2016)).”
Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization (2016, background): “…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 goodness-of-ﬁt-based regions (Bertsimas et al. (2014)).”
Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach (2016, background): “Bertsimas, Gupta, and Kallus [12, 11] develop uncertainty sets based on various linear and higher-order moment conditions.”