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We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…
In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
We present a block gradient ascent method for solving the quantum optimal transport problem with entropic regularisation similar to the algorithm proposed in [D. Feliciangeli, A. Gerolin, L. Portinale: J. Funct. Anal. 285 (2023), no. 4,…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…
The martingale part in the semimartingale decomposition of a Brownian motion with respect to an enlargement of its filtration, is an anticipative mapping of the given Brownian motion. In analogy to optimal transport theory, we define causal…
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…
Point sets matching problems can be handled by optimal transport. The mechanism behind it is that optimal transport recovers the point-to-point correspondence associated with the least curl deformation. Optimal transport is a special form…
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…
In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…
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…
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…
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…
A fundamental concept in optimal transport is c-cyclical monotonicity: it allows to link the optimality of transport plans to the geometry of their support sets. Recently, related concepts have been successfully applied in the…
This paper considers the decentralized consensus optimization problem defined over a network where each node holds a second-order differentiable local objective function. Our goal is to minimize the summation of local objective functions…
Entropic regularization is a method for large-scale linear programming. Geometrically, one traces intersections of the feasible polytope with scaled toric varieties, starting at the Birch point. We compare this to log-barrier methods, with…
In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been…