Related papers: Dual Regularized Optimal Transport
The problem of robust distributed control arises in several large-scale systems, such as transportation networks and power grid systems. In many practical scenarios controllers might not have enough information to make globally optimal…
We address the issue of safe optimal path planning under parametric uncertainties using a novel regularizer that allows trading off optimality with safety. The proposed regularizer leverages the notion that collisions may be modeled as…
Optimal transport (OT) theory provides powerful tools to compare probability measures. However, OT is limited to nonnegative measures having the same mass, and suffers serious drawbacks about its computation and statistics. This leads to…
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence…
The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by [9,11]. We show that the dual formulation of this problem is valid in a context…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph…
We present a distributionally robust optimization (DRO) approach for the transmission expansion planning problem, considering both long- and short-term uncertainties on the system demand and non-dispatchable renewable generation. On the…
Many exciting robotic applications require multiple robots with many degrees of freedom, such as manipulators, to coordinate their motion in a shared workspace. Discovering high-quality paths in such scenarios can be achieved, in principle,…
A new data-enabled control technique for uncertain linear time-invariant systems, recently conceived by Coulson et\ al., builds upon the direct optimization of controllers over input/output pairs drawn from a large dataset. We adopt an…
Optimal transport is a powerful framework for computing distances between probability distributions. We unify the two main approaches to optimal transport, namely Monge-Kantorovitch and Sinkhorn-Cuturi, into what we define as Tsallis…
Although optimal transport (OT) problems admit closed form solutions in a very few notable cases, e.g. in 1D or between Gaussians, these closed forms have proved extremely fecund for practitioners to define tools inspired from the OT…
Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
We introduce fast algorithms for generalized unnormalized optimal transport. To handle densities with different total mass, we consider a dynamic model, which mixes the $L^p$ optimal transport with $L^p$ distance. For $p=1$, we derive 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…
The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g. single-cell genomics) or used to…
This paper presents a distributed, optimal, communication-aware trajectory planning algorithm for multi-robot systems. Building on prior work, it addresses the multi-robot communication-aware trajectory planning problem using a general…
The topic of this study lies in the intersection of two fields. One is related with analyzing transport phenomena in complicated flows.For this purpose, we use so-called coherent sets: non-dispersing, possibly moving regions in the flow's…
Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function,…