Related papers: Adaptive Optimal Transport
This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…
A new method is proposed for the solution of the data-driven optimal transport barycenter problem and of the more general distributional barycenter problem that the article introduces. The method improves on previous approaches based on…
During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been…
We study the problem of aligning the supports of distributions. Compared to the existing work on distribution alignment, support alignment does not require the densities to be matched. We propose symmetric support difference as a divergence…
In this work, we develop a distributed source routing algorithm for topology discovery suitable for ISP transport networks, that is however inspired by opportunistic algorithms used in ad hoc wireless networks. We propose a plug-and-play…
In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative…
The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs-Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature…
This paper considers the distributed optimization of a sum of locally observable, non-convex functions. The optimization is performed over a multi-agent networked system, and each local function depends only on a subset of the variables. An…
We present a neural framework for learning conditional optimal transport (OT) maps between probability distributions. Our approach introduces a conditioning mechanism capable of processing both categorical and continuous conditioning…
We propose a method that enables practitioners to conveniently incorporate custom non-decomposable performance metrics into differentiable learning pipelines, notably those based upon neural network architectures. Our approach is based on…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
Robotic systems must be able to quickly and robustly make decisions when operating in uncertain and dynamic environments. While Reinforcement Learning (RL) can be used to compute optimal policies with little prior knowledge about the…
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…
Optimal transport is a powerful framework for the efficient allocation of resources between sources and targets. However, traditional models often struggle to scale effectively in the presence of large and heterogeneous populations. In this…
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…
Adversarial examples, crafted by adding perturbations imperceptible to humans, can deceive neural networks. Recent studies identify the adversarial transferability across various models, \textit{i.e.}, the cross-model attack ability of…
The traffic assignment problem is essential for traffic flow analysis, traditionally solved using mathematical programs under the Equilibrium principle. These methods become computationally prohibitive for large-scale networks due to…