Related papers: Deep Semi-Martingale Optimal Transport
Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for…
We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between $m$ discrete probability distributions supported each on $n$…
We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: ``Heuristics'' and approaches with a more sound mathematical justification,…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
Recently, the problem of local minima in very high dimensional non-convex optimization has been challenged and the problem of saddle points has been introduced. This paper introduces a dynamic type of normalization that forces the system to…
We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal…
The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which is closest to the Brownian motion. Recent contributions have…
In this paper, we introduce a generalized dynamical unbalanced optimal transport framework by incorporating limited control input and mass dissipation, addressing limitations in conventional optimal transport for control applications. We…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
In this paper, we unroll the dynamics of the dual ascent (DA) algorithm in two coupled graph neural networks (GNNs) to solve constrained optimization problems. The two networks interact with each other at the layer level to find a saddle…
We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…
We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
Inspired by the Boltzmann kinetics, we propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
In this paper, we consider the optimal coordination of automated vehicles at intersections under fixed crossing orders. We formulate the problem using direct optimal control and exploit the structure to construct a semi-distributed…
The basic problem of optimal transportation consists in minimizing the expected costs $\mathbb {E}[c(X_1,X_2)]$ by varying the joint distribution $(X_1,X_2)$ where the marginal distributions of the random variables $X_1$ and $X_2$ are…
We introduce an extension of the Optimal Transport problem when multiple costs are involved. Considering each cost as an agent, we aim to share equally between agents the work of transporting one distribution to another. To do so, we…
We formulate a dynamic reinsurance problem in which the insurer seeks to control the terminal distribution of its surplus while minimizing the L2-norm of the ceded risk. Using techniques from martingale optimal transport, we show that,…