Optimal transport in systems and control

Y Chen, TT Georgiou, M Pavon - Annual Review of Control …, 2021‏ - annualreviews.org
Optimal transport began as the problem of how to efficiently redistribute goods between
production and consumers and evolved into a far-reaching geometric variational framework …

Proximal optimal transport modeling of population dynamics

C Bunne, L Papaxanthos, A Krause… - International …, 2022‏ - proceedings.mlr.press
We propose a new approach to model the collective dynamics of a population of particles
evolving with time. As is often the case in challenging scientific applications, notably single …

Multi-marginal optimal transport and probabilistic graphical models

I Haasler, R Singh, Q Zhang… - IEEE Transactions on …, 2021‏ - ieeexplore.ieee.org
We study multi-marginal optimal transport problems from a probabilistic graphical model
perspective. We point out an elegant connection between the two when the underlying cost …

Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descent

J Altschuler, S Chewi, PR Gerber… - Advances in Neural …, 2021‏ - proceedings.neurips.cc
We study first-order optimization algorithms for computing the barycenter of Gaussian
distributions with respect to the optimal transport metric. Although the objective is …

Wasserstein barycenters are NP-hard to compute

JM Altschuler, E Boix-Adsera - SIAM Journal on Mathematics of Data Science, 2022‏ - SIAM
Computing Wasserstein barycenters (aka optimal transport barycenters) is a fundamental
problem in geometry which has recently attracted considerable attention due to many …

On the linear convergence of the multimarginal Sinkhorn algorithm

G Carlier - SIAM Journal on Optimization, 2022‏ - SIAM
The aim of this note is to give an elementary proof of linear convergence of the Sinkhorn
algorithm for the entropic regularization of multimarginal optimal transport in the setting of …

Polynomial-time algorithms for multimarginal optimal transport problems with structure

JM Altschuler, E Boix-Adsera - Mathematical Programming, 2023‏ - Springer
Abstract Multimarginal Optimal Transport (MOT) has attracted significant interest due to
applications in machine learning, statistics, and the sciences. However, in most applications …

The multimarginal optimal transport formulation of adversarial multiclass classification

NG Trillos, M Jacobs, J Kim - Journal of Machine Learning Research, 2023‏ - jmlr.org
We study a family of adversarial multiclass classification problems and provide equivalent
reformulations in terms of: 1) a family of generalized barycenter problems introduced in the …

On the complexity of the optimal transport problem with graph-structured cost

J Fan, I Haasler, J Karlsson… - … conference on artificial …, 2022‏ - proceedings.mlr.press
Multi-marginal optimal transport (MOT) is a generalization of optimal transport to multiple
marginals. Optimal transport has evolved into an important tool in many machine learning …

Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey

A Khamis, R Tsuchida, M Tarek… - … on Pattern Analysis …, 2024‏ - ieeexplore.ieee.org
Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth
century and has led to a plethora of methods for answering many theoretical and applied …