Related papers: Optimal Transport with Proximal Splitting
The dynamic formulation of optimal transport has attracted growing interests in scientific computing and machine learning, and its computation requires to solve a PDE-constrained optimization problem. The classical Eulerian discretization…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
Optimization is at the heart of machine learning, statistics and many applied scientific disciplines. It also has a long history in physics, ranging from the minimal action principle to finding ground states of disordered systems such as…
In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the…
We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two…
This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function…
We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…
In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with…
Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the system state itself. In this paper, we establish the pathwise…
This paper develops a unified distributed method for solving two classes of constrained networked optimization problems, i.e., optimal consensus problem and resource allocation problem with non-identical set constraints. We first transform…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
We consider stochastic convex optimization problems with affine constraints and develop several methods using either primal or dual approach to solve it. In the primal case, we use a special penalization technique to make the initial…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and…
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…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
In this paper, a decentralized proximal method of multipliers (DPMM) is proposed to solve constrained convex optimization problems over multi-agent networks, where the local objective of each agent is a general closed convex function, and…