Related papers: Optimal Transport of Information
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
We suggest a new way of defining optimal transport of positive-semidefinite matrix-valued measures. It is inspired by a recent rendering of the incompressible Euler equations and related conservative systems as concave maximization…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
We study an information-structure design problem (a.k.a. persuasion) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal distributions. As in the standard…
We study information design settings where the designer controls information about a state, and there are multiple agents interacting in a game who are privately informed about their types. Each agent's utility depends on all agents' types…
We consider a routing game among non-atomic agents where link latency functions are conditional on an uncertain state of the network. The agents have the same prior belief about the state, but only a fixed fraction receive private route…
Bayesian approaches developed to solve the optimal design of sequential experiments are mathematically elegant but computationally challenging. Recently, techniques using amortization have been proposed to make these Bayesian approaches…
Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neuralnetwork method is advocated…
In this paper we study optimal advertising problems that models the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we…
We study Monge's optimal transportation problem, where the cost is given by optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the…
Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into…
The tradeoff relation between speed and cost is a central issue in designing fast and efficient information processing devices. We derive an achievable bound on thermodynamic cost for obtaining information through finite-time…
Motivated by robust dynamic resource allocation in operations research, we study the \textit{Online Learning to Transport} (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw…
Bayesian optimization is a methodology for global optimization of unknown and expensive objectives. It combines a surrogate Bayesian regression model with an acquisition function to decide where to evaluate the objective. Typical regression…
We propose a model to describe the optimal distributions of residents and services in a prescribed urban area. The cost functional takes into account the transportation costs (according to a Monge--Kantorovich-type criterion) and two…
We introduce folded optimal transport, as a method to extend a cost or distance defined on the extreme boundary of a convex to the whole convex, related to convex extension. This construction broadens the framework of standard optimal…
An important question in the field of AI is the extent to which successful behaviour requires an internal representation of the world. In this work, we quantify the amount of information an optimal policy provides about the underlying…
We study the regularity of solutions to an optimal transportation problem where the dimension of the source is larger than that of the target. We demonstrate that if the target is $c$-convex, then the source has a canonical foliation whose…
We study an information design problem with two informed senders and a receiver in which, in contrast to traditional Bayesian persuasion settings, senders do not have commitment power. In our setting, a trusted mediator/platform gathers…
We provide a framework to approximate the 2-Wasserstein distance and the optimal transport map, amenable to efficient training as well as statistical and geometric analysis. With the quadratic cost and considering the Kantorovich dual form…