Related papers: Order Constraints in Optimal Transport
Urban transportation is a complex phenomenon. Since many agents are constantly interacting in parallel, it is difficult to predict the future state of a transportation system. Because of this, optimization techniques tend to give obsolete…
In this paper, we explore a scenario where a sender provides an information policy and a receiver, upon observing a realization of this policy, decides whether to take a particular action, such as making a purchase. The sender's objective…
We consider the model of a transportation problem with the objective of finding a minimum-cost transportation plan for shipping a given commodity from a set of supply centers to the customers. Since the exact values of supply and demand and…
Optimal transport has been one of the most exciting subjects in mathematics, starting from the 18th century. As a powerful tool to transport between two probability measures, optimal transport methods have been reinvigorated nowadays in a…
This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…
The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by…
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
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…
We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constrictions, conceptualized as toll stations at specified…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…
Public transport is vital for meeting people's mobility needs. Providers need to plan their services well to offer high quality and low cost. Optimized planning can benefit providers, customers, and municipalities. The planning process for…
There is a relatively small amount of research covering urban freight movements. Most research dealing with the subject of urban mobility focuses on passenger vehicles, not commercial vehicles hauling freight. However, in many ways, urban…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
Many real-life optimization problems frequently contain one or more constraints or objectives for which there are no explicit formulas. If data is however available, these data can be used to learn the constraints. The benefits of this…
Transformers have achieved state-of-the-art performance in numerous tasks. In this paper, we propose a continuous-time formulation of transformers. Specifically, we consider a dynamical system whose governing equation is parametrized by…
Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…
We propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special type. We propose some kind of "algebra" on different models and corresponding…
Optimal transport is a framework that facilitates the most efficient allocation of a limited amount of resources. However, the most efficient allocation scheme does not necessarily preserve the most fairness. In this paper, we establish a…
Optimal transport (OT) theory describes general principles to define and select, among many possible choices, the most efficient way to map a probability measure onto another. That theory has been mostly used to estimate, given a pair of…
We study a multimodal journey planning scenario consisting of a public transit network and a transfer graph which represents a secondary transportation mode (e.g., walking, cycling, e-scooter). The objective is to compute Pareto-optimal…