Related papers: Accelerating Motion Planning via Optimal Transport
We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between $m$ discrete probability distributions supported each on $n$…
This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation. There is hence the need for fast…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
Partial Optimal Transport (POT) addresses the problem of transporting only a fraction of the total mass between two distributions, making it suitable when marginals have unequal size or contain outliers. While Sinkhorn-based methods are…
Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also…
We propose Mirror Descent Optimal Transport (MDOT), a novel method for solving discrete optimal transport (OT) problems with high precision, by unifying temperature annealing in entropic-regularized OT (EOT) with mirror descent techniques.…
Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex…
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…
Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly…
We study the multi-marginal partial optimal transport (POT) problem between $m$ discrete (unbalanced) measures with at most $n$ supports. We first prove that we can obtain two equivalence forms of the multimarginal POT problem in terms of…
Multimarginal optimal transport (MOT) is a powerful framework for modeling interactions between multiple distributions, yet its applicability is bottlenecked by a high computational overhead. Entropic regularization provides computational…
We consider the numerical solution of the discrete multi-marginal optimal transport (MOT) by means of the Sinkhorn algorithm. In general, the Sinkhorn algorithm suffers from the curse of dimensionality with respect to the number of…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
Safe path planning is a crucial component in autonomous robotics. The many approaches to find a collision free path can be categorically divided into trajectory optimisers and sampling-based methods. When planning using occupancy maps, 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…
Trajectory optimization methods for motion planning attempt to generate trajectories that minimize a suitable objective function. Such methods efficiently find solutions even for high degree-of-freedom robots. However, a globally optimal…
This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete martingale optimal transport (MOT) problem. Moreover, as the…
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…
Optimal transport (OT) is a widely used tool in machine learning, but computing high-accuracy solutions for large instances remains costly. Entropic regularization and the Sinkhorn algorithm improve scalability; however, when the…
In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional…