Related papers: The entropic optimal (self-)transport problem: Lim…
The growing amount of fluctuating renewable infeeds and market liberalization increases uncertainty in power system operation. To capture the influence of fluctuations in operational planning, we model the forecast errors of the uncertain…
In this paper, we study the Entropic Martingale Optimal Transport (EMOT) problem on \mathbb{R}. The investigation of the EMOT problem arises in the calibration problem of the Stochastic Volatility Models, where martingale constraints…
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…
We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. This defines a stochastic linear program for which, under general conditions, we characterize the fluctuations…
When a parameter of interest is defined to be a nondifferentiable transform of a regular parameter, the parameter does not have an influence function, rendering the existing theory of semiparametric efficient estimation inapplicable.…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
Sample-based trajectory optimisers are a promising tool for the control of robotics with non-differentiable dynamics and cost functions. Contemporary approaches derive from a restricted subclass of stochastic optimal control where the…
Sinkhorn algorithm is the de-facto standard approximation algorithm for optimal transport, which has been applied to a variety of applications, including image processing and natural language processing. In theory, the proof of its…
Optimization problems with stochastic dominance constraints provide a possibility to shape risk by selecting a benchmark random outcome with a desired distribution. The comparison of the relevant random outcomes to the respective benchmarks…
Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on…
We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by establishing dimension-free, parametric rates for…
Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…
We study the problem of bounding path-dependent expectations (within any finite time horizon $d$) over the class of discrete-time martingales whose marginal distributions lie within a prescribed tolerance of a given collection of benchmark…
In 2013, Cuturi [Cut13] introduced the Sinkhorn algorithm for matrix scaling as a method to compute solutions to regularized optimal transport problems. In this paper, aiming at a better convergence rate for a high accuracy solution, we…
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…
The Sinkhorn algorithm is a numerical method for the solution of optimal transport problems. Here, I give a brief survey of this algorithm, with a strong emphasis on its geometric origin: it is natural to view it as a discretization, by…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
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 formulate a class of velocity-free finite-particle methods for mass transport problems based on a time-discrete incremental variational principle that combines entropy and the cost of particle transport, as measured by the Wasserstein…
The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…