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We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…

Statistics Theory · Mathematics 2021-06-01 Liyan Xie , Rui Gao , Yao Xie

Wasserstein distributionally robust optimization (WDRO) attempts to learn a model that minimizes the local worst-case risk in the vicinity of the empirical data distribution defined by Wasserstein ball. While WDRO has received attention as…

Machine Learning · Statistics 2020-06-23 Yongchan Kwon , Wonyoung Kim , Joong-Ho Won , Myunghee Cho Paik

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

This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several…

Optimization and Control · Mathematics 2023-07-04 Yanqin Fan , Hyeonseok Park , Gaoqian Xu

The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…

Machine Learning · Computer Science 2026-02-10 Eduardo Figueiredo , Steven Adams , Luca Laurenti

We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…

Statistics Theory · Mathematics 2020-04-30 Jonathan Niles-Weed , Quentin Berthet

We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures…

Methodology · Statistics 2018-02-15 Jose Blanchet , Lin Chen , Xun Yu Zhou

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

We use distributionally-robust optimization for machine learning to mitigate the effect of data poisoning attacks. We provide performance guarantees for the trained model on the original data (not including the poison records) by training…

Machine Learning · Computer Science 2020-01-30 Farhad Farokhi

We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…

Mathematical Finance · Quantitative Finance 2020-05-27 Stephan Eckstein , Michael Kupper , Mathias Pohl

We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a…

Optimization and Control · Mathematics 2021-01-28 Viet Anh Nguyen , Soroosh Shafieezadeh-Abadeh , Daniel Kuhn , Peyman Mohajerin Esfahani

This paper discusses a class of combinatorial optimization problems with uncertain costs in the objective function. It is assumed that a sample of the cost realizations is available, which defines an empirical probability distribution for…

Optimization and Control · Mathematics 2023-12-21 Marcel Jackiewicz , Adam Kasperski , Pawel Zielinski

Neural networks are vulnerable to adversarial examples and researchers have proposed many heuristic attack and defense mechanisms. We address this problem through the principled lens of distributionally robust optimization, which guarantees…

Machine Learning · Statistics 2020-05-04 Aman Sinha , Hongseok Namkoong , Riccardo Volpi , John Duchi

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…

Optimization and Control · Mathematics 2024-02-07 Hong T. M. Chu , Meixia Lin , Kim-Chuan Toh

This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…

Optimization and Control · Mathematics 2026-02-05 Chung-Han Hsieh

We propose a distributionally robust classification model with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-$\infty$ Wasserstein ambiguity set centered at…

Machine Learning · Computer Science 2021-07-13 Yijie Wang , Viet Anh Nguyen , Grani A. Hanasusanto

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

We consider the problem of learning from training data obtained in different contexts, where the underlying context distribution is unknown and is estimated empirically. We develop a robust method that takes into account the uncertainty of…

Machine Learning · Statistics 2022-02-18 Muhammad Osama , Dave Zachariah , Petre Stoica

Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…

Machine Learning · Statistics 2020-07-07 Hossein Taheri , Ramtin Pedarsani , Christos Thrampoulidis

In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…

Machine Learning · Statistics 2022-05-31 Tim Tsz-Kit Lau , Han Liu