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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,…
Over the past few years, ride-sharing has emerged as an effective way to relieve traffic congestion. A key problem for these platforms is to come up with a revenue-optimal (or GMV-optimal) pricing scheme and an induced vehicle dispatching…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
We address the problem of identifying the dynamical law governing the evolution of a population of indistinguishable particles, when only aggregate distributions at successive times are observed. Assuming a Markovian evolution on a discrete…
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…
This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
We study Sinkhorn's algorithm for solving the entropically regularized optimal transport problem. Its iterate $\pi_{t}$ is shown to satisfy $H(\pi_{t}|\pi_{*})+H(\pi_{*}|\pi_{t})=O(t^{-1})$ where $H$ denotes relative entropy and $\pi_{*}$…
The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…
We analyze two algorithms for approximating the general optimal transport (OT) distance between two discrete distributions of size $n$, up to accuracy $\varepsilon$. For the first algorithm, which is based on the celebrated Sinkhorn's…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
Comparing probability distributions is a fundamental problem in data sciences. Simple norms and divergences such as the total variation and the relative entropy only compare densities in a point-wise manner and fail to capture the geometric…
We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…
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…
Estimating mutual information is an important statistics and machine learning problem. To estimate the mutual information from data, a common practice is preparing a set of paired samples $\{(\mathbf{x}_i,\mathbf{y}_i)\}_{i=1}^n…
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 (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
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,…
Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…