Related papers: Optimal Transport of Information
The structure of naming systems in natural languages hinges on a trade-off between high informativeness and low complexity. Prior work capitalizes on information theory to formalize these notions; however, these studies generally rely on…
We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality…
In the current book I suggest an off-road path to the subject of optimal transport. I tried to avoid prior knowledge of analysis, PDE theory and functional analysis, as much as possible. Thus I concentrate on discrete and semi-discrete…
We present a mathematical framework and computational methods to optimally design a finite number of sequential experiments. We formulate this sequential optimal experimental design (sOED) problem as a finite-horizon partially observable…
Bayesian optimization is a methodology to optimize black-box functions. Traditionally, it focuses on the setting where you can arbitrarily query the search space. However, many real-life problems do not offer this flexibility; in…
Let $\mathcal{V}$ be the set of all combinations of expected value of finite objective functions from designing information. I showed that $\mathcal{V}$ is a compact and convex set implemented by signal structures with finite support when…
We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching…
It is well-known that plug-in statistical estimation of optimal transport suffers from the curse of dimensionality. Despite recent efforts to improve the rate of estimation with the smoothness of the problem, the computational complexity of…
Categorization is an important topic both for biological and artificial neural networks. Here, we take an information theoretic approach to assess the efficiency of the representations induced by category learning. We show that one can…
A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a…
Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically…
We investigate a two-period Bayesian persuasion game, where the receiver faces a decision, akin to a one-armed bandit problem: to undertake an action, gaining noisy information and a corresponding positive or negative payoff, or to refrain.…
We study the use of Bayesian persuasion (i.e., strategic use of information disclosure/signaling) in endogenous team formation. This is an important consideration in settings such as crowdsourcing competitions, open science challenges and…
There has been a recent surge of interest in the role of information in strategic interactions. Much of this work seeks to understand how the realized equilibrium of a game is influenced by uncertainty in the environment and the information…
I describe a Bayesian persuasion problem where Receiver has a private type representing a cutoff for choosing Sender's preferred action, and Sender has maxmin preferences over all Receiver type distributions with known mean and bounds. This…
We study causal optimal transport in continuous time, with Markovian cost, between a finite-state Markov source and a diffusion target. By replacing the source with its conditional law given the observation of the target, we characterize…
We study information design in multi-agent systems (MAS) with binary actions and strategic complementarities, where an external designer influences behavior only through signals. Agents play the smallest-equilibrium of the induced Bayesian…
Complex robot navigation and control problems can be framed as policy search problems. However, interactive learning in uncertain environments can be expensive, requiring the use of data-efficient methods. Bayesian optimization is an…
Addressing uncertainty is critical for autonomous systems to robustly adapt to the real world. We formulate the problem of model uncertainty as a continuous Bayes-Adaptive Markov Decision Process (BAMDP), where an agent maintains a…
We prove existence and uniqueness results for solutions to a class of optimal transportation problems with infinitely many marginals, supported on the real line. We also provide a characterization of the solution with an explicit formula.…