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We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…
Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing appropriate probability distributions based on observed data is critical for…
We study a variety of Wasserstein distributionally robust optimization (WDRO) problems where the distributions in the ambiguity set are chosen by constraining their Wasserstein discrepancies to the empirical distribution. Using the notion…
In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the…
Using only retrospective data, we study the problem of predicting treatment effects for the same treatment/policy implemented in a different location or time period. We propose a distributionally robust estimator that minimizes the…
We consider decision-making problems under decision-dependent uncertainty (DDU), where the distribution of uncertain parameters depends on the decision variables and is only observable through a finite offline dataset. To address this…
The paper studies the robustness properties of discrete-time stochastic optimal control under Wasserstein model approximation for both discounted-cost and average-cost criteria. Specifically, we study the performance loss when applying an…
Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance. Despite its recent empirical success in operations research and machine…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
We study distributionally robust chance-constrained programs (DRCCPs) with individual chance constraints under a Wasserstein ambiguity. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…
This paper deals with the estimation of a probability measure on the real line from data observed with an additive noise. We are interested in rates of convergence for the Wasserstein metric of order $p\geq 1$. The distribution of the…
Distributionally robust optimization (DRO) is an effective approach for data-driven decision-making in the presence of uncertainty. Geometric uncertainty due to sampling or localized perturbations of data points is captured by Wasserstein…
We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…
Distributionally robust supervised learning (DRSL) is emerging as a key paradigm for building reliable machine learning systems for real-world applications -- reflecting the need for classifiers and predictive models that are robust to the…
We consider a discrete time stochastic Markovian control problem under model uncertainty. Such uncertainty not only comes from the fact that the true probability law of the underlying stochastic process is unknown, but the parametric family…
The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on…
In finite mixtures of location-scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a…