Related papers: On Linear Optimization over Wasserstein Balls
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered…
Wasserstein distances are widely used in modern data analysis but pose significant computational and statistical challenges in high dimensions. The sliced Wasserstein distance alleviates these challenges by leveraging one-dimensional…
Wasserstein barycenter, built on the theory of optimal transport, provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it…
This paper is a continuation of our accompanying paper [Talbi, Touzi and Zhang (2021)], where we characterized the mean field optimal stopping problem by an obstacle equation on the Wasserstein space of probability measures, provided that…
Computing Wasserstein barycenters of discrete measures has recently attracted considerable attention due to its wide variety of applications in data science. In general, this problem is NP-hard, calling for practical approximative…
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…
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…
Robust estimation is an important problem in statistics which aims at providing a reasonable estimator when the data-generating distribution lies within an appropriately defined ball around an uncontaminated distribution. Although minimax…
Reinforcement learning algorithms, though successful, tend to over-fit to training environments hampering their application to the real-world. This paper proposes $\text{W}\text{R}^{2}\text{L}$ -- a robust reinforcement learning algorithm…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of probability measures with finite support. In this paper, we show that finding a barycenter of sparse support is hard, even in dimension 2 and…
We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
Given a prior probability density $p$ on a compact set $K$ we characterize the probability distribution $q_{\delta}^*$ on $K$ contained in a Wasserstein ball $B_{\delta}(\mu)$ centered in a given discrete measure $\mu$ for which the…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
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…
We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…
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…
This paper focuses on the Wasserstein distributionally robust mean-lower semi-absolute deviation (DR-MLSAD) model, where the ambiguity set is a Wasserstein ball centered on the empirical distribution of the training sample. This model can…