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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…
This paper studies the equitable and optimal transport (EOT) problem, which has many applications such as fair division problems and optimal transport with multiple agents etc. In the discrete distributions case, the EOT problem can be…
The performance of optimization algorithms relies crucially on their parameterizations. Finding good parameter settings is called algorithm tuning. The sequential parameter optimization (SPOT) package for R is a toolbox for tuning and…
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 applications, and its multi-marginal extension opens up for…
Alignment plays a fundamental role in many machine learning problems, such as multi-network analysis, multimodal learning, and point cloud registration. Recent works increasingly leverage optimal transport (OT) for distributional alignment,…
We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss…
Regularized discrete optimal transport (OT) is a powerful tool to measure the distance between two discrete distributions that have been constructed from data samples on two different domains. While it has a wide range of applications in…
Most common Optimal Transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. However, it is sometimes relevant to work only with moments of measures instead of the measure itself, and many…
Preference learning in Large Language Models (LLMs) has advanced significantly, yet existing methods remain limited by modest performance gains, high computational costs, hyperparameter sensitivity, and insufficient modeling of global…
Deep clustering, which learns representation and semantic clustering without labels information, poses a great challenge for deep learning-based approaches. Despite significant progress in recent years, most existing methods focus on…
This paper addresses the practical challenge in Entropic Optimal Transport (EOT) where the underlying ground cost function is typically latent and unobserved. Rather than assuming a fixed geometric cost, we adopt a data-driven approach…
Optimal-Transport Distributionally Robust Optimization (OT-DRO) robustifies data-driven decision-making under uncertainty by capturing the sampling-induced statistical error via optimal transport ambiguity sets. The standard OT-DRO pipeline…
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 (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…
In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass,…
In the research of Intelligent Transportation Systems (ITS), traffic simulation is a key procedure for the evaluation of new methods and optimization of strategies. However, existing traffic simulation systems face two challenges. First,…
The recent end-to-end neural solvers have shown promise for small-scale routing problems but suffered from limited real-time scaling-up performance. This paper proposes GLOP (Global and Local Optimization Policies), a unified hierarchical…
In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to…