Related papers: Computing Optimal Transport Plans via Min-Max Grad…
Min-max optimization problems (i.e., min-max games) have attracted a great deal of attention recently as their applicability to a wide range of machine learning problems has become evident. In this paper, we study min-max games with…
We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out…
We study a multi-agent decision problem in large population games. Agents from multiple populations select strategies for repeated interactions with one another. At each stage of these interactions, agents use their decision-making model to…
We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…
The LogSumExp function, dual to the Kullback-Leibler (KL) divergence, plays a central role in many important optimization problems, including entropy-regularized optimal transport (OT) and distributionally robust optimization (DRO). In…
We study the consequences of the equivalence between the least gradient problem and a boundary-to-boundary optimal transport problem in two dimensions. We extend the relationship between the two problems to their respective dual problems,…
In noncooperative Nash games, equilibria are often inefficient. This is exemplified by the Prisoner's Dilemma and was first provably shown in the 1980s. Since then, understanding the quality of Nash equilibrium (NE) received considerable…
In this paper, we propose a multi-player extension of the minimum cost flow problem inspired by a transportation problem that arises in modern transportation industry. We associate one player with each arc of a directed network, each trying…
A growing body of work in game theory extends the traditional Stackelberg game to settings with one leader and multiple followers who play a Nash equilibrium. Standard approaches for computing equilibria in these games reformulate the…
We present an efficient algorithm for regularized optimal transport. In contrast to previous methods, we use the Douglas-Rachford splitting technique to develop an efficient solver that can handle a broad class of regularizers. The…
We propose a framework for two-player infinite-dimensional games with cooperative or competitive structure. These games take the form of coupled partial differential equations in which players optimize over a space of measures, driven by…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a…
We investigate the convergence properties of a continuous-time optimization method, the \textit{Mean-Field Best Response} flow, for solving convex-concave min-max games with entropy regularization. We introduce suitable Lyapunov functions…
In the paper we show that an important class of multistage traffic equillibrium models (including correspondence matrix calculation, traffic assignment problem etc) and their economic generalizations can be considered as proper population…
In this work, we solve a discrete optimal transport problem in a nonuniform environment. To solve the optimal transport problem, we build the cost matrix and then use classical solvers for discrete optimal transport. The challenge is to…
Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special convex-concave structure. While some recent…