Data-driven risk-averse stochastic optimization with Wasserstein metric

By Chaoyue Zhao, Yongpei Guan. Operations Research Letters, 2018

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Quantifying Distributional Model Risk via Optimal Transport (2016, unknown): “…and Love (2015) for KL-divergence and other likelihood based uncertainty sets, Pflug and Wozabal (2007); Wozabal (2012); Esfahani and Kuhn (2015); Zhao and Guan (2015); Gao and Kleywegt (2016) for Wasserstein distance based neighborhoods, Erdoğan and Iyengar (2006) for neighborhoods based on…”
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning (2019, background): “Reformulations of these models as nonconvex optimization problems as well approximations that were discovered in [60, 113] and signiﬁcantly generalized in [12, 38].”
Distributionally Robust Optimization: A Review (2019, methodology): “(Jiang and Guan [167, Theorems 1–2], Rahimian et al. [251, Proposition 3], Shapiro [289]) For a fixed x ∈ X , we have sup P∈PTV(P0; ) EP [ h(x, ξ̃) ] = EP0 [ h(x, ξ̃) ] , = 0, ν- ess sups∈Ξ h(x, ξ̃(s)) + (1− )CVaRP0 [ h(x, ξ̃) ] , 0 < < 1, ν- ess sups∈Ξ h(x, ξ̃(s)), ≥ 1, where ν- ess sups∈Ξ h(x, ξ̃”
Distributionally Robust Stochastic Optimization with Wasserstein Distance (2016, methodology): “In both Esfahani and Kuhn [17], Zhao and Guan [53] only p= 1 is considered.”