Related papers: Computing Optimal Transport Plans via Min-Max Grad…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
We study a nonlinear multimarginal optimal transport problem arising in risk management, where the objective is to maximize a spectral risk measure of the pushforward of a coupling by a cost function. Although this problem is inherently…
The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We consider both the balanced and unbalanced problem and show in…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
Min cut is an important graph partitioning method. However, current solutions to the min cut problem suffer from slow speeds, difficulty in solving, and often converge to simple solutions. To address these issues, we relax the min cut…
We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth…
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…
We present an inverse dynamic game-based algorithm to learn parametric constraints from a given dataset of local Nash equilibrium interactions between multiple agents. Specifically, we introduce mixed-integer linear programs (MILP) encoding…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…
We consider the traffic control problem of dynamic routing over parallel servers, which arises in a variety of engineering systems such as transportation and data transmission. We propose a semi-gradient, on-policy algorithm that learns an…
We derive iterative scaling algorithms of the Sinkhorn-Knopp (SK) type for constrained optimal transport. The constraints are in the form of prior-imposed zeroes in the transport plan. Based on classical Bregman arguments, we prove…
Motivated by emerging resource allocation and data placement problems such as web caches and peer-to-peer systems, we consider and study a class of resource allocation problems over a network of agents (nodes). In this model, nodes can…
In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing…
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,…
Adversarial formulations such as generative adversarial networks (GANs) have rekindled interest in two-player min-max games. A central obstacle in the optimization of such games is the rotational dynamics that hinder their convergence. In…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
We consider a network equilibrium model (i.e. a combined model), which was proposed as an alternative to the classic four-step approach for travel forecasting in transportation networks. This model can be formulated as a convex minimization…
As the title suggests, this is the third paper in a series addressing bilevel optimization problems that are governed by the Kantorovich problem of optimal transport. These tasks can be reformulated as mathematical problems with…