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Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
This paper considers the decentralized (discrete) optimal transport (D-OT) problem. In this setting, a network of agents seeks to design a transportation plan jointly, where the cost function is the sum of privately held costs for each…
This paper introduces two variational formulations for a model of robust optimal transport, that is, the problem of designing optimal transport networks that are resilient to potential damages, balancing construction costs against the…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…
Deep neural networks (DNNs) often produce overconfident predictions on out-of-distribution (OOD) inputs, undermining their reliability in open-world environments. Singularities in semi-discrete optimal transport (OT) mark regions of…
In this work, we study the classical distributed optimization problem over digraphs, where the objective function is a sum of smooth local functions. Inspired by the implicit tracking mechanism proposed in our earlier work, we develop a…
In this paper, we develop unrolled neural networks to solve constrained optimization problems, offering accelerated, learnable counterparts to dual ascent (DA) algorithms. Our framework, termed constrained dual unrolling (CDU), comprises…
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…
Metropolitan scale vehicular traffic modeling is used by a variety of private and public sector urban mobility stakeholders to inform the design and operations of road networks. High-resolution stochastic traffic simulators are increasingly…
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…
This paper addresses the fundamental problem of non-uniform area coverage in multi-agent systems, where different regions require varying levels of attention due to mission-dependent priorities. Existing uniform coverage strategies are…
We study dynamical optimal transport of discrete time systems (dDOT) with Lagrangian cost. The problem is approached by combining optimal control and Kantorovich duality theory. Based on the derived solution, a first order splitting…
In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…
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…
Differential drive robots are widely used in various scenarios thanks to their straightforward principle, from household service robots to disaster response field robots. There are several types of driving mechanisms for real-world…
This paper addresses an Optimal Transport (OT)-based efficient multi-robot exploration problem, considering the energy constraints of a multi-robot system. The efficiency in this problem implies how a team of robots (agents) covers a given…
Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…
The goal of this paper is to introduce a new theoretical framework for Optimal Transport (OT), using the terminology and techniques of Fully Probabilistic Design (FPD). Optimal Transport is the canonical method for comparing probability…
Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…