Distributionally Robust Optimization and Its Tractable Approximations

By Joel Goh, Melvyn Sim. 2010

770 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Certifying Some Distributional Robustness with Principled Adversarial Training (2017, background): “…have considered ﬁnite-dimensional parametrizations for P , such as constraint sets for moments, support, or directional deviations [17, 20, 27], as well as non-parametric distances for probability measures such as f -divergences [5, 6, 40, 44, 21, 47], and Wasserstein distances [23, 59,…”
How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks (2020, methodology): “Distributional robustness considers small adversarial perturbations of the data distribution, and ensures that the model performs well under these (Goh & Sim, 2010; Sagawa et al., 2020; Sinha et al., 2018; Staib & Jegelka, 2019).”
Deep Long-Tailed Learning: A Survey (2021, background): “DRO-LT [110] extended the prototypical contrastive learning with distribution robust optimization [150], which makes the learned model more robust to data distribution shift.”
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);…”
Distributionally Robust Convex Optimization (2014, background): “We now prove that the nesting condition is also necessary for tractability.”
Kullback-Leibler divergence constrained distributionally robust optimization (2012, methodology): “The basic idea of solving Problem (3) is to implement the duality theory of convex optimization, which is a key tool in robust optimization and has been used frequently in DRO; see, e.g., Delage and Ye (2010) and Goh and Sim (2010).”
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).”
A practical guide to robust optimization (2015, background): “For multistage problems, Goh and Sim (2010) show how to construct uncertainty sets based on, e.g., the covariance matrix or bounds on the expected value.”
Robust Markov Decision Processes (2013, background): “[4], Goh and Sim [10]) to reduce the approximation error via piecewise affine approximations of the reward to-go function.”
Robust stochastic optimization for reservoir operation (2015, background): “4 and ROME (Robust Optimization Made Easy) developed by Goh and Sim [2011].”
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.”
Certifiable Distributional Robustness with Principled Adversarial Training (2017, background): “…have considered ﬁnite-dimensional parametrizations for P , such as constraint sets for moments, support, or directional deviations [14, 17, 21], as well as non-parametric distances for probability measures such as f -divergences [4, 5, 32, 29, 18, 35], and Wasserstein distances [8, 19,…”
Distributionally Robust Markov Decision Processes (2010, background): “, Popescu [26], Delage and Ye [12], Calafiore and El Ghaoui [10], and Goh and Sim [18]).”
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…”
Distributionally Robust Optimization: A Review (2019, methodology): “Similarly, we define W and W∗.”