Related papers: Optimal Transport and Skorokhod Embedding
We develop an explicit non-randomized solution to the Skorokhod embedding problem in an abstract setup of signed functionals of Markovian excursions. Our setting allows to solve the Skorokhod embedding problem, in particular, for diffusions…
We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This…
We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree-structured graphs with…
We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also…
We propose a new framework for formulating optimal transport distances between Markov chains. Previously known formulations studied couplings between the entire joint distribution induced by the chains, and derived solutions via a reduction…
We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function. The result is based on the geometric notion of cyclical invariance and inspired by the…
We study optimal transport between probability measures supported on the same finite metric space, where the ground cost is a distance induced by a weighted connected graph. Building on recent work showing that the resulting Kantorovich…
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…
Since their introduction, anchoring methods in extragradient-type saddlepoint problems have inspired a flurry of research due to their ability to provide order-optimal rates of accelerated convergence in very general problem settings. Such…
We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class…
In classical optimal transport, the contributions of Benamou-Brenier and McCann regarding the time-dependent version of the problem are cornerstones of the field and form the basis for a variety of applications in other mathematical areas.…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
We formulate an optimal switching problem when the underlying filtration is generated by a marked point process and a Brownian motion. Each mode is characterized by a different compensator for the point process, and thus by a different…
Motivated by a new formulation of the classical dividend problem, we show that Peskir's maximality principle can be transferred to singular stochastic control problems with 2-dimensional degenerate dynamics and absorption along the diagonal…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…
We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality…
It is well known that given two probability measures $\mu$ and $\nu$ on $\mathbb{R}$ in convex order there exists a discrete-time martingale with these marginals. Several solutions are known (for example from the literature on the Skorokhod…
We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Using Transportation Cost Inequalities for stochastic…