Related papers: Point source localisation with unbalanced optimal …
We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost…
Gradient-based optimization methods are the most popular choice for finding local optima for classical minimization and saddle point problems. Here, we highlight a systemic issue of gradient dynamics that arise for saddle point problems,…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data's underlying geometry. Choosing such…
This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the…
Branched Optimal Transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route,…
This paper presents an optimization-based receding horizon trajectory planning algorithm for dynamical systems operating in unstructured and cluttered environments. The proposed approach is a two-step procedure that uses a motion planning…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…
We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport. These estimators represent the measure of interest as the pushforward of a chosen reference…
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…
To remedy the drawbacks of full-mass or fixed-mass constraints in classical optimal transport, we propose adaptive optimal transport which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It…
We investigate the continuous optimal transport problem in the so-called Kantorovich form, i.e. given two Radon measures on two compact sets, we seek an optimal transport plan which is another Radon measure on the product of the sets that…
Imbalanced data pose challenges for deep learning based classification models. One of the most widely-used approaches for tackling imbalanced data is re-weighting, where training samples are associated with different weights in the loss…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
This paper presents GRT, a domain-independent heuristic planning system for STRIPS worlds. GRT solves problems in two phases. In the pre-processing phase, it estimates the distance between each fact and the goals of the problem, in a…
This paper presents a triple optimization algorithm of two-dimensional space, driving path and driving speed, and iterates in the time dimension to obtain the local optimal solution of path and speed in the optimal driving area. Design…
We present a novel approach to path planning for robotic manipulators, in which paths are produced via iterative optimisation in the latent space of a generative model of robot poses. Constraints are incorporated through the use of…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
Unsupervised change detection between airborne LiDAR data points, taken at separate times over the same location, can be difficult due to unmatching spatial support and noise from the acquisition system. Most current approaches to detect…