Related papers: Optimal Transport: Fast Probabilistic Approximatio…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
We propose a centralized transportation system that integrates public transit with ridesharing to provide multimodal transportation. At each time interval, the system receives a set of personal drivers, designated drivers, and public…
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…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
Approximate K Nearest Neighbor (AKNN) search in high-dimensional spaces is a critical yet challenging problem. In AKNN search, distance computation is the core task that dominates the runtime. Existing approaches typically use approximate…
The geometric transportation problem takes as input a set of points $P$ in $d$-dimensional Euclidean space and a supply function $\mu : P \to \mathbb{R}$. The goal is to find a transportation map, a non-negative assignment $\tau : P \times…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
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…
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of…
Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…
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 present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…
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 propose a sampling-based trajectory optimization methodology for constrained problems. We extend recent works on stochastic search to deal with box control constraints,as well as nonlinear state constraints for discrete dynamical…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…