arXiv research

New method designs fairer transport plans with uncertainty.

NOT learns optimal transport plans, kernel costs improve performance.

Sliced-regularized OT improves transport plan accuracy.

The paper examines properties of GW optimal transport plans, showing they can be sparse and permutation-supported.

Bayesian approach to optimal transport with stochastic costs.

Study shows how optimal transport behaves in higher dimensions.

Deep learning improves trip prediction accuracy in transportation planning.

Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approxima…

Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans $π_1, π_2, \ldots$ converges weakly to a transport plan $π$, then $π$ is also optimal (between its marginals). Alfonsi, Corbetta and Jourdain asked whether the same property is true for th…

We give an alternative proof for the fact that in $n$-dimensional Alexandrov spaces with curvature bounded below there exists a unique optimal transport plan from any purely $(n-1)$-unrectifiable starting measure, and that this plan is induced by an optimal map.

Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into account traffic congestion effects is the first topic, and it shows various links with…

The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing statistical OT as that of learning the transport plan's kernel mean embedding from sam…

In this paper we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two periods model. In particular, we consider the optimal transport plan constructed in \cite{HobsonKlimmek2013} as well as the one introduced in \cite{BeiglJuil} and further studi…

We tackle the challenge of disentangled representation learning in generative adversarial networks (GANs) from the perspective of regularized optimal transport (OT). Specifically, a smoothed OT loss gives rise to an implicit transportation plan between the latent space and the data space. Based on this theoretical obse…

Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the Sinkhorn algorithm. However, entropy keeps the transportation plan strictly positive…

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regularization is added to the problem, the transportation plan can be…

Enhanced route planning with probabilistic prediction and uncertainty sets.

New approach to sparse optimal transport for matching tokens with experts.

Extends subspace detour method to Gromov-Wasserstein problem.

Efficiently predicts optimal transport plans using sliced potentials.

New algorithm ensures fair matching in resource allocation.

New framework formalizes estimating valid transport maps, revealing their statistical limits.

Characterizes Forman curvature bounds and proves curvature equivalence.

Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.

We study a single-period optimal transport problem on $\mathbb{R}^2$ with a covariance-type cost function $c(x,y) = (x_1-y_1)(x_2-y_2)$ and a backward martingale constraint. We show that a transport plan $γ$ is optimal if and only if there is a maximal monotone set $G$ that supports the $x$-marginal of $γ$ and such tha…

Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of sliced Wasserstein distances), solve the OT problem between these reduced measures, a…

Proposes FROT for high-dimensional data, avoiding curse of dimensionality.

A new method for fast optimal transport using sliced Wasserstein generalized geodesics.

New optimal transport method handles mass creation and destruction.

UNOT solves optimal transport problems efficiently using neural networks.

The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.

We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a…

This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Sev…

We prove that in metric measure spaces where the entropy functional is K-convex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures with finite second moments lives on a non-branching set of geodesics. As a corollary we obtain that in these spaces there exists only one opti…

This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two distributions. To that end, we propose a stochastic dual approach of regularize…

Study improves traffic prediction intervals for minor roads.

We explore the use of deep learning and deep reinforcement learning for optimization problems in transportation. Many transportation system analysis tasks are formulated as an optimization problem - such as optimal control problems in intelligent transportation systems and long term urban planning. Often transportation…

Efficiently estimates optimal transport maps with rigorous guarantees.

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterparts, our method promotes couplings with low transport rank, a new struct…

We propose an SDP relaxation for the Gromov-Wasserstein distance, providing globally optimal solutions.

New methods estimate transport-growth pairs in unbalanced optimal transport.

COPT optimizes graph distances via simultaneous optimal transport.

Develop a framework for barycentric projections of optimal transport plans on Riemannian manifolds.

We introduce a new framework for optimal transport using Schatten-p regularization to recover low-rank structures.

A new method optimizes slicing directions for SW distances to improve high-dimensional probability measure comparison.

A new model corrects inhomogeneity in Optimal Transport with Boundary.

Optimal transport adapted for contaminated probabilities, showing equivalence under specific conditions.

Novel proof shows continuity of optimal transport feasible set mapping.