Related papers: General auction method for real-valued optimal tra…
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…
This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…
The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
This paper examines knapsack auctions as a method to solve the knapsack problem with incomplete information, where object values are private and sizes are public. We analyze three auction types-uniform price (UP), discriminatory price (DP),…
We study an abstract optimal auction problem for a single good or service. This problem includes environments where agents have budgets, risk preferences, or multi-dimensional preferences over several possible configurations of the good…
Optimal transport is a framework that facilitates the most efficient allocation of a limited amount of resources. However, the most efficient allocation scheme does not necessarily preserve the most fairness. In this paper, we establish a…
Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are…
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…
Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…
Auction is the common paradigm for resource allocation which is a fundamental problem in human society. Existing research indicates that the two primary objectives, the seller's revenue and the allocation efficiency, are generally…
We study the classical weighted perfect matchings problem for bipartite graphs or sometimes referred to as the assignment problem, i.e., given a weighted bipartite graph $G = (U\cup V,E)$ with weights $w : E \rightarrow \mathcal{R}$ we are…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
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…
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…
Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two…
The majority of online marketplaces offer promotion programs to sellers to acquire additional customers for their products. These programs typically allow sellers to allocate advertising budgets to promote their products, with higher…
We propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special type. We propose some kind of "algebra" on different models and corresponding…
To support a freight carrier in a combinatorial transport auction, we proposes an exact and two heuristic strategies for bidding on subsets of requests. The exact bidding strategy is based on the concept of elementary request combinations.…
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…
In this paper, we consider fair assignment of complex requests for Mobility-On-Demand systems. We model the transportation requests as temporal logic formulas that must be satisfied by a fleet of vehicles. We require that the assignment of…