Related papers: Bisimulation Metrics are Optimal Transport Distanc…
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
We study the synthesis of a policy in a Markov decision process (MDP) following which an agent reaches a target state in the MDP while minimizing its total discounted cost. The problem combines a reachability criterion with a discounted…
Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify…
In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems where the residence time on each state is described by a generic…
Platooning connected and autonomous vehicles (CAVs) provide significant benefits in terms of traffic efficiency and fuel economy. However, most existing platooning systems assume the availability of pre-determined plans, which is not…
Intelligent transportation systems have recently emerged to address the growing interest for safer, more efficient, and sustainable transportation solutions. In this direction, this paper presents distributed algorithms for control and…
Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…
Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved…
We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the…
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.…
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…
We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…
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 develop a new methodology for model-based clustering. Optimizing the log-likelihood provides a principled statistical framework for clustering, with solutions found via the EM algorithm. However, because the log-likelihood is nonconvex,…
We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…
We consider Monge-Kantorovich optimal transport problems on $\mathbb{R}^d$, $d\ge 1$, with a convex cost function given by the cumulant generating function of a probability measure. Examples include the Wasserstein-2 transport whose cost…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
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…