Related papers: Sinkhorn Algorithm for Sequentially Composed Optim…
In 2012, Pflug and Pichler proved, under regularity assumptions, that the value function in Multistage Stochastic Programming (MSP) is Lipschitz continuous w.r.t. the Nested Distance, which is a distance between scenario trees (or discrete…
The mismatch capacity characterizes the highest information rate of the channel under a prescribed decoding metric and serves as a critical performance indicator in numerous practical communication scenarios. Compared to the commonly used…
Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…
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…
This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform…
In this note, we generalize the classical optimal partial transport (OPT) problem by modifying the mass destruction/creation term to function-based terms, introducing what we term ``generalized optimal partial transport'' problems. We then…
Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However,…
Solving large scale entropic optimal transport problems with the Sinkhorn algorithm remains challenging, and domain decomposition has been shown to be an efficient strategy for problems on large grids. Unbalanced optimal transport is a…
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and…
We show that a solution of the optimal assignment problem can be obtained as the limit of the solution of an entropy maximization problem, as a deformation parameter tends to infinity. This allows us to apply entropy maximization algorithms…
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or…
We propose a discrete time formulation of the semi martingale optimal transport problembased on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by Guo et…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
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…
Imitation learning algorithms have been interpreted as variants of divergence minimization problems. The ability to compare occupancy measures between experts and learners is crucial in their effectiveness in learning from demonstrations.…
We study an entropic optimal transport problem in which the transport plan is penalized by a nonlinear convex functional acting on the coupling. We establish existence, uniqueness, and uniform a priori bounds for minimizers, and we show…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…
Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two…
Vector-quantized networks (VQNs) have exhibited remarkable performance across various tasks, yet they are prone to training instability, which complicates the training process due to the necessity for techniques such as subtle…