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Inverse Reinforcement Learning (IRL) aims to recover a reward function from expert demonstrations. Recently, Optimal Transport (OT) methods have been successfully deployed to align trajectories and infer rewards. While OT-based methods have…

机器学习 · 计算机科学 2025-06-10 Zixuan Dong , Yumi Omori , Keith Ross

We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…

Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This…

统计理论 · 数学 2024-03-12 Francisco Andrade , Gabriel Peyre , Clarice Poon

In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal-dual regularization, the authors propose to…

最优化与控制 · 数学 2023-07-12 Stefano Cipolla , Jacek Gondzio , Filippo Zanetti

In this paper, we consider Strassen's version of optimal transport (OT) problem, which concerns minimizing the excess-cost probability (i.e., the probability that the cost is larger than a given value) over all couplings of two given…

概率论 · 数学 2022-02-22 Lei Yu

Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications. In this work, we propose a novel OT formulation that takes feature correlations into account…

机器学习 · 计算机科学 2021-10-08 Pratik Jawanpuria , N T V Satyadev , Bamdev Mishra

This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary differential equation (ODE). This naturally yields an algorithm to…

数值分析 · 数学 2025-04-07 Luca Nenna , Daniyar Omarov , Brendan Pass

We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph…

机器学习 · 计算机科学 2023-11-23 Shoichiro Takeda , Yasunori Akagi , Naoki Marumo , Kenta Niwa

Optimal transport (OT) and maximum mean discrepancies (MMD) are now routinely used in machine learning to compare probability measures. We focus in this paper on \emph{Sinkhorn divergences} (SDs), a regularized variant of OT distances which…

统计理论 · 数学 2019-10-16 Aude Genevay , Lénaic Chizat , Francis Bach , Marco Cuturi , Gabriel Peyré

Although Sinkhorn divergences are now routinely used in data sciences to compare probability distributions, the computational effort required to compute them remains expensive, growing in general quadratically in the size $n$ of the support…

机器学习 · 统计学 2020-10-27 Meyer Scetbon , Marco Cuturi

Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the…

最优化与控制 · 数学 2025-04-10 Keiichi Morikuni , Koya Sakakibara , Asuka Takatsu

Sinkhorn's algorithm is a method of choice to solve large-scale optimal transport (OT) problems. In this context, it involves an inverse temperature parameter $\beta$ that determines the speed-accuracy trade-off. To improve this trade-off,…

机器学习 · 计算机科学 2024-08-22 Lénaïc Chizat

Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…

统计理论 · 数学 2024-05-14 Tao Wang , Ziv Goldfeld

In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization…

最优化与控制 · 数学 2017-09-27 Pavel Dvurechensky , Alexander Gasnikov , Sergey Omelchenko , Alexander Tiurin

In several applications, including imaging of deformable objects while in motion, simultaneous localization and mapping, and unlabeled sensing, we encounter the problem of recovering a signal that is measured subject to unknown…

信息论 · 计算机科学 2021-03-15 Yanting Ma , Petros T. Boufounos , Hassan Mansour , Shuchin Aeron

We provide theoretical analyses for two algorithms that solve the regularized optimal transport (OT) problem between two discrete probability measures with at most $n$ atoms. We show that a greedy variant of the classical Sinkhorn…

数据结构与算法 · 计算机科学 2021-07-27 Tianyi Lin , Nhat Ho , Michael I. Jordan

Rapidly growing product lines and services require a finer-granularity forecast that considers geographic locales. However the open question remains, how to assess the quality of a spatio-temporal forecast? In this manuscript we introduce a…

机器学习 · 统计学 2017-12-08 Lucas Roberts , Leo Razoumov , Lin Su , Yuyang Wang

This paper studies the convergence rates of optimal transport (OT) map estimators, a topic of growing interest in statistics, machine learning, and various scientific fields. Despite recent advancements, existing results rely on regularity…

统计理论 · 数学 2024-12-12 Yizhe Ding , Runze Li , Lingzhou Xue

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…

机器学习 · 计算机科学 2024-04-24 Yikun Bai , Ivan Medri , Rocio Diaz Martin , Rana Muhammad Shahroz Khan , Soheil Kolouri

Optimal transport (OT) theory provides powerful tools to compare probability measures. However, OT is limited to nonnegative measures having the same mass, and suffers serious drawbacks about its computation and statistics. This leads to…

机器学习 · 统计学 2021-01-26 Tam Le , Truyen Nguyen