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Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…

Machine Learning · Computer Science 2020-02-21 Marin Ballu , Quentin Berthet , Francis Bach

Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein…

Optimization and Control · Mathematics 2023-03-24 Waïss Azizian , Franck Iutzeler , Jérôme Malick

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

Machine Learning · Statistics 2024-11-05 Daniel Kuhn , Peyman Mohajerin Esfahani , Viet Anh Nguyen , Soroosh Shafieezadeh-Abadeh

We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…

Optimization and Control · Mathematics 2021-10-20 Yu Mei , Jia Liu , Zhiping Chen

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…

Optimization and Control · Mathematics 2017-06-14 Peyman Mohajerin Esfahani , Daniel Kuhn

Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…

Machine Learning · Statistics 2025-11-12 Changyu Liu , Yuling Jiao , Junhui Wang , Jian Huang

Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…

Optimization and Control · Mathematics 2020-10-01 Iman Shames , Farhad Farokhi

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

Optimization and Control · Mathematics 2018-05-21 Viet Anh Nguyen , Daniel Kuhn , Peyman Mohajerin Esfahani

Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that generalization guarantees of…

Optimization and Control · Mathematics 2025-01-28 Tam Le , Jérôme Malick

Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…

Statistics Theory · Mathematics 2021-03-04 Jose Blanchet , Karthyek Murthy , Nian Si

Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models.…

Machine Learning · Computer Science 2024-08-23 Jie Wang , Rui Gao , Yao Xie

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…

Machine Learning · Computer Science 2022-01-26 Yaodong Yu , Tianyi Lin , Eric Mazumdar , Michael I. Jordan

This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics.…

Machine Learning · Statistics 2024-10-30 Jérémie Bigot , Paul Freulon , Boris P. Hejblum , Arthur Leclaire

Wasserstein distributionally robust optimization (WDRO) optimizes against worst-case distributional shifts within a specified uncertainty set, leading to enhanced generalization on unseen adversarial examples, compared to standard…

Machine Learning · Computer Science 2025-03-07 Shuang Liu , Yihan Wang , Yifan Zhu , Yibo Miao , Xiao-Shan Gao

Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between…

Machine Learning · Computer Science 2020-11-02 Rui Gao , Xi Chen , Anton J. Kleywegt

We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…

Machine Learning · Computer Science 2025-03-27 Francesco Micheli , Efe C. Balta , Anastasios Tsiamis , John Lygeros

Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data…

Optimization and Control · Mathematics 2026-02-09 Siyi Wang , Zifan Wang , Karl H. Johansson

This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…

Optimization and Control · Mathematics 2023-01-13 Charles Dapogny , Franck Iutzeler , Andrea Meda , Boris Thibert

Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…

Optimization and Control · Mathematics 2026-05-28 Tam Le

We investigate a stochastic program with expected value constraints, addressing the problem in a general context through Distributionally Robust Optimization (DRO) approach using Wasserstein distances, where the ambiguity set depends on the…

Optimization and Control · Mathematics 2023-04-18 Diego Fonseca , Mauricio Junca
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