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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

We introduce the notion of Worst-Case Sensitivity, defined as the worst-case rate of increase in the expected cost of a Distributionally Robust Optimization (DRO) model when the size of the uncertainty set vanishes. We show that worst-case…

Econometrics · Economics 2020-10-22 Jun-ya Gotoh , Michael Jong Kim , Andrew E. B. Lim

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

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If…

Optimization and Control · Mathematics 2015-12-02 Soroosh Shafieezadeh-Abadeh , Peyman Mohajerin Esfahani , Daniel Kuhn

We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…

Optimization and Control · Mathematics 2024-06-18 Nicolas Lanzetti , Antonio Terpin , Florian Dörfler

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…

Systems and Control · Electrical Eng. & Systems 2026-03-10 Yichen Zhou , Yanglei Song , Serdar Yüksel

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…

Optimization and Control · Mathematics 2019-05-27 Emilie Chouzenoux , Henri Gérard , Jean-Christophe Pesquet

We investigate model risk distributionally robust sensitivities for functionals on the Wasserstein space when the underlying model is constrained to the martingale class and/or is subject to constraints on the first marginal law. Our…

Mathematical Finance · Quantitative Finance 2025-11-05 Nathan Sauldubois , Nizar Touzi

This paper addresses a novel \emph{cost-sensitive} distributionally robust log-optimal portfolio problem, where the investor faces \emph{ambiguous} return distributions, and a general convex transaction cost model is incorporated. The…

Optimization and Control · Mathematics 2024-11-01 Chung-Han Hsieh , Xiao-Rou Yu

Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same…

Optimization and Control · Mathematics 2020-06-16 Johannes Wiebe , Inês Cecílio , Jonathan Dunlop , Ruth Misener

Graphs are playing a crucial role in different fields since they are powerful tools to unveil intrinsic relationships among signals. In many scenarios, an accurate graph structure representing signals is not available at all and that…

Machine Learning · Computer Science 2021-05-14 Xiang Zhang , Yinfei Xu , Qinghe Liu , Zhicheng Liu , Jian Lu , Qiao Wang

Robustness studies of black-box models is recognized as a necessary task for numerical models based on structural equations and predictive models learned from data. These studies must assess the model's robustness to possible…

Optimization and Control · Mathematics 2022-09-26 Marouane Il Idrissi , Nicolas Bousquet , Fabrice Gamboa , Bertrand Iooss , Jean-Michel Loubes

Despite of its importance for safe machine learning, uncertainty quantification for neural networks is far from being solved. State-of-the-art approaches to estimate neural uncertainties are often hybrid, combining parametric models with…

Machine Learning · Computer Science 2021-12-03 Joachim Sicking , Maram Akila , Maximilian Pintz , Tim Wirtz , Asja Fischer , Stefan Wrobel

We consider the problem of analyzing the probabilistic performance of first-order methods when solving convex optimization problems drawn from an unknown distribution only accessible through samples. By combining performance estimation…

Optimization and Control · Mathematics 2025-12-11 Jisun Park , Vinit Ranjan , Bartolomeo Stellato

In this paper, we apply the framework of optimal transport to the formulation of optimal design problems. By considering the Wasserstein space as a set of design variables, we associate each probability measure with a shape configuration of…

Optimization and Control · Mathematics 2025-09-08 Fumiya Okazaki , Takayuki Yamada

We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance…

Machine Learning · Computer Science 2026-05-08 Vinit Ranjan , Jisun Park , Bartolomeo Stellato

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

We consider a general online stochastic optimization problem with multiple budget constraints over a horizon of finite time periods. In each time period, a reward function and multiple cost functions are revealed, and the decision maker…

Machine Learning · Computer Science 2022-07-26 Jiashuo Jiang , Xiaocheng Li , Jiawei Zhang

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

We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when…

Optimization and Control · Mathematics 2026-01-30 Brandon Tam , Silvana M. Pesenti