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We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex…

Optimization and Control · Mathematics 2021-06-28 Jia-Jie Zhu , Wittawat Jitkrittum , Moritz Diehl , Bernhard Schölkopf

Distributionally robust optimization (DRO) has emerged as a powerful paradigm for reliable decision-making under uncertainty. This paper focuses on DRO with ambiguity sets defined via the Sinkhorn discrepancy: an entropy-regularized…

Machine Learning · Statistics 2025-12-16 Jie Wang

We review distributionally robust optimization (DRO), a principled approach for constructing statistical estimators that hedge against the impact of deviations in the expected loss between the training and deployment environments. Many…

Methodology · Statistics 2024-01-29 Jose Blanchet , Jiajin Li , Sirui Lin , Xuhui Zhang

We introduce a new framework, Bayesian Distributionally Robust Optimization (Bayesian-DRO), for data-driven stochastic optimization where the underlying distribution is unknown. Bayesian-DRO contrasts with most of the existing DRO…

Optimization and Control · Mathematics 2023-02-10 Alexander Shapiro , Enlu Zhou , Yifan Lin

Distributionally Robust Optimization (DRO) is a worst-case approach to decision making when there is model uncertainty. It is also well known that for certain uncertainty sets, DRO is approximated by a regularized nominal problem. We show…

Optimization and Control · Mathematics 2026-05-08 Jun-ya Gotoh , Michael Jong Kim , Andrew E. B. Lim

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying…

Optimization and Control · Mathematics 2022-10-25 Hamed Rahimian , Sanjay Mehrotra

We consider the problem of distributionally robust multimodal machine learning. Existing approaches often rely on merging modalities on the feature level (early fusion) or heuristic uncertainty modeling, which downplays modality-aware…

Machine Learning · Computer Science 2025-11-11 Peilin Yang , Yu Ma

Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making…

Optimization and Control · Mathematics 2022-04-04 Yuxiao Chen , Jip Kim , James Anderson

In this work, we present an algorithmically tractable safe approximation of distributionally robust optimization (DRO) problems that contain univariate indicator functions. The latter appear in different applications, but render the model…

Optimization and Control · Mathematics 2026-01-22 Jana Dienstbier , Frauke Liers , Florian Rösel , Jan Rolfes

This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…

Machine Learning · Statistics 2021-08-23 Ruidi Chen , Ioannis Ch. Paschalidis

Distributionally robust optimization (DRO) can improve the robustness and fairness of learning methods. In this paper, we devise stochastic algorithms for a class of DRO problems including group DRO, subpopulation fairness, and empirical…

Machine Learning · Computer Science 2025-02-03 Tasuku Soma , Khashayar Gatmiry , Sharut Gupta , Stefanie Jegelka

Distributionally robust optimization (DRO) has shown lot of promise in providing robustness in learning as well as sample based optimization problems. We endeavor to provide DRO solutions for a class of sum of fractionals, non-convex…

Machine Learning · Computer Science 2022-06-01 Avinandan Bose , Arunesh Sinha , Tien Mai

Distributionally Robust Optimization (DRO) has been shown to provide a flexible framework for decision making under uncertainty and statistical estimation. For example, recent works in DRO have shown that popular statistical estimators can…

Machine Learning · Statistics 2020-04-21 Jose Blanchet , Yang Kang , Fan Zhang , Zhangyi Hu

Distributionally robust optimization (DRO) is a powerful framework for training robust models against data distribution shifts. This paper focuses on constrained DRO, which has an explicit characterization of the robustness level. Existing…

Machine Learning · Statistics 2024-04-02 Qi Zhang , Yi Zhou , Ashley Prater-Bennette , Lixin Shen , Shaofeng Zou

Distributionally robust optimization (DRO) is a powerful technique to train robust models against data distribution shift. This paper aims to solve regularized nonconvex DRO problems, where the uncertainty set is modeled by a so-called…

Optimization and Control · Mathematics 2025-06-30 Yufeng Yang , Yi Zhou , Zhaosong Lu

A central goal of machine learning is to learn robust representations that capture the causal relationship between inputs features and output labels. However, minimizing empirical risk over finite or biased datasets often results in models…

Machine Learning · Computer Science 2021-06-15 Chunting Zhou , Xuezhe Ma , Paul Michel , Graham Neubig

Distributionally robust optimization is used to tackle decision making problems under uncertainty where the distribution of the uncertain data is ambiguous. Many ambiguity sets have been proposed for continuous uncertainty that build on…

Optimization and Control · Mathematics 2025-05-28 Karthik Natarajan , Divya Padmanabhan , Arjun Ramachandra

In this paper, we consider a network capacity expansion problem in the context of telecommunication networks, where there is uncertainty associated with the expected traffic demand. We employ a distributionally robust stochastic…

Optimization and Control · Mathematics 2020-04-10 Trivikram Dokka , Francis Garuba , Marc Goerigk , Peter Jacko

Single-level reformulations of (non-convex) distributionally robust optimization (DRO) problems are often intractable, as they contain semiinfinite dual constraints. Based on such a semiinfinite reformulation, we present a safe…

Optimization and Control · Mathematics 2025-06-09 J. Dienstbier , F. Liers , J. Rolfes

Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of…

Optimization and Control · Mathematics 2022-05-03 Rui Gao , Anton J. Kleywegt