English
Related papers

Related papers: Multi-marginal Optimal Transport with a Tree-struc…

200 papers

We propose the Entropic-regularized Robust Optimal Transport (E-ROBOT) framework, a novel method that combines the robustness of ROBOT with the computational and statistical benefits of entropic regularization. We show that, rooted in the…

Machine Learning · Statistics 2025-09-16 Davide La Vecchia , Hang Liu

We propose a family of relaxations of the optimal transport problem which regularize the problem by introducing an additional minimization step over a small region around one of the underlying transporting measures. The type of…

Machine Learning · Statistics 2019-06-11 Saied Mahdian , Jose Blanchet , Peter Glynn

Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…

Machine Learning · Statistics 2014-03-25 Marco Cuturi

Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning…

Machine Learning · Statistics 2023-04-17 Tianlin Liu , Joan Puigcerver , Mathieu Blondel

Classical entropy regularization is poorly suited to continuous-time martingale transport, since relative entropy between diffusion laws typically forces their volatility characteristics to coincide. We introduce a specific-entropy…

Probability · Mathematics 2026-05-22 Francois Buet-Golfouse , Anaïs Després , Zhenjie Ren , Xin Zhang

The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…

Machine Learning · Computer Science 2024-07-04 Kirill Neklyudov , Rob Brekelmans , Alexander Tong , Lazar Atanackovic , Qiang Liu , Alireza Makhzani

This short paper announces the main results of \cite{SBB2026}, where the Schr\"odinger--Bass Bridge (SBB) problem is introduced and studied in full generality. Here we provide a direct PDE derivation of the SBB system in dimension one,…

A Schr\"{o}dinger bridge establishes a dynamic transport map between two target distributions via a reference process, simultaneously solving an associated entropic optimal transport problem. We consider the setting where samples from the…

Machine Learning · Computer Science 2025-01-22 Stefano Peluchetti

We study the potential functions that determine the optimal density for $\varepsilon$-entropically regularized optimal transport, the so-called Schr\"odinger potentials, and their convergence to the counterparts in classical optimal…

Analysis of PDEs · Mathematics 2021-11-02 Marcel Nutz , Johannes Wiesel

We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal…

Optimization and Control · Mathematics 2018-10-16 Matthias Liero , Alexander Mielke , Giuseppe Savaré

We study the regularity properties of the minimisers of entropic optimal transport providing a natural analogue of the $\varepsilon$-regularity theory of quadratic optimal transport in the entropic setting. More precisely, we show that if…

Analysis of PDEs · Mathematics 2025-01-14 Rishabh S. Gvalani , Lukas Koch

The offset optimization problem seeks to coordinate and synchronize the timing of traffic signals throughout a network in order to enhance traffic flow and reduce stops and delays. Recently, offset optimization was formulated into a…

Optimization and Control · Mathematics 2020-04-28 Yi Ouyang , Richard Y. Zhang , Javad Lavaei , Pravin Varaiya

We study the inverse optimal transport problem of recovering the ground cost from an optimal transport plan. In discrete settings, this problem reduces to inverse linear programming and is intrinsically ill-posed, exhibiting…

Optimization and Control · Mathematics 2026-04-27 Gabriel Peyré , Clarice Poon , Oscar Tron

A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…

Classical Analysis and ODEs · Mathematics 2020-09-04 Alessio Brancolini , Benedikt Wirth

We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals $N$ and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible…

Optimization and Control · Mathematics 2025-01-15 Simone Di Marino , Mathieu Lewin , Luca Nenna

The Schr\"odinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorithm is widely used to solve the static optimal transport…

Machine Learning · Statistics 2025-10-28 Ibuki Maeda , Rentian Yao , Atsushi Nitanda

The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…

Optimization and Control · Mathematics 2024-06-24 Asmaa Eldesoukey , Olga Movilla Miangolarra , Tryphon T. Georgiou

We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…

Numerical Analysis · Mathematics 2020-04-01 Carolin Dirks , Benedikt Wirth

We propose a variational formulation of an inverse problem in continuous-time stochastic control, aimed at identifying control costs consistent with a given distribution over trajectories. The formulation is based on minimizing the…

Optimization and Control · Mathematics 2026-03-19 Yumiharu Nakano

We formulate and study an optimal transportation problem with infinitely many marginals; this is a natural extension of the multi-marginal problem studied by Gangbo and Swiech (1998). We prove results on the existence, uniqueness and…

Analysis of PDEs · Mathematics 2012-06-26 Brendan Pass