Related papers: Variational Transport: A Convergent Particle-Based…
Controlling the $\mathcal W_\infty$ Wasserstein distance by the $\mathcal W_p$ Wasserstein distance is interesting both for theorical and numerical applications. A first paper on this problem was written several years ago [3]. Some year…
We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads to a complicated stochastic optimization problem where the…
In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $\phi$-divergences and Wasserstein distances, respectively. While the former focuses on ambiguity in…
Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown…
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement…
Discriminating between distributions is an important problem in a number of scientific fields. This motivated the introduction of Linear Optimal Transportation (LOT), which embeds the space of distributions into an $L^2$-space. The…
We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…
We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization,…
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…
We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…
We introduce an architecture for variational quantum algorithms that can be efficiently trained via parameter updates along exact geodesics on the Riemannian state manifold. This features a parameter-optimal circuit ansatz which supersedes…
We investigate the problem of pairwise multi-marginal optimal transport, that is, given a collection of probability distributions $\{P_\alpha\}$ on a Polish space $\mathcal{X}$, to find a coupling $\{X_\alpha\}$, $X_\alpha\sim P_\alpha$,…
We study the contraction in Wasserstein distance of the coordinate ascent variational inference algorithm. This is shown to hold under a transport-information inequality at the fixed points and a functional smoothness condition. The results…
We propose a novel method for comparing non-aligned graphs of different sizes, based on the Wasserstein distance between graph signal distributions induced by the respective graph Laplacian matrices. Specifically, we cast a new formulation…
A new Wasserstein multi-element polynomial chaos expansion (WPCE) is proposed, which is inspired by recent advances in computational optimal transport for estimating Wasserstein distances. The developed method combines unsupervised learning…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…
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…
We develop a discrete optimal transport framework for analyzing simulated annealing algorithms on finite state spaces. Building on the discrete Wasserstein metric introduced by Maas (J. Funct. Anal., 2011), we define a generalized discrete…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…