Continuous Random Variable Estimation is not Optimal for the Witsenhausen Counterexample - ETIS, équipe ICI Accéder directement au contenu
Communication Dans Un Congrès Année : 2021

Continuous Random Variable Estimation is not Optimal for the Witsenhausen Counterexample

Résumé

Optimal design of distributed decision policies can be a difficult task, illustrated by the famous Witsenhausen counterexample. In this paper we characterize the optimal control designs for the vector-valued setting assuming that it results in an interim state, i.e. the result of the first decision maker action, that can be described by a continuous random variable which has a probability density function. More specifically, we provide a genie-aided outer bound that relies on our previous results for empirical coordination problems. This solution turns out to be not optimal in general, since it consists of a time-sharing strategy between two linear schemes of specific power. It follows that the optimal decision strategy for the original scalar Witsenhausen problem must lead to an interim state that cannot be described by a continuous random variable which has a probability density function.
Fichier principal
Vignette du fichier
20210510082500_596523_1708.pdf (167.81 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03223047 , version 1 (10-05-2021)
hal-03223047 , version 2 (19-05-2021)

Identifiants

  • HAL Id : hal-03223047 , version 1

Citer

Mael Le Treust, Tobias J Oechtering. Continuous Random Variable Estimation is not Optimal for the Witsenhausen Counterexample. IEEE ISIT 2021, Jul 2021, melbourne, Australia. ⟨hal-03223047v1⟩
66 Consultations
60 Téléchargements

Partager

Gmail Facebook X LinkedIn More