Independently randomized symmetric policies are optimal for exchangeable stochastic teams with infinitely many decision makers

Name: Independently randomized symmetric policies are optimal for exchangeable stochastic teams with infinitely many decision makers
Author: Sanjari, S., Saldı, Naci, Yüksel, S.

İsim	Independently randomized symmetric policies are optimal for exchangeable stochastic teams with infinitely many decision makers
Yazar	Sanjari, S., Saldı, Naci, Yüksel, S.
Basım Tarihi:	2020-12-14
Basım Yeri	- IEEE
Tür	Belge
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0743-1546
Kayıt Numarası	8d9e719f-01d7-44f2-b0b1-066ea0a4a11d
Lokasyon	Natural and Mathematical Sciences
Tarih	2020-12-14
Notlar	Natural Sciences and Engineering Research Council (NSERC) of Canada
Örnek Metin	We study stochastic team (known also as decentralized stochastic control or identical interest stochastic game) problems with large or countably infinite number of decision makers, and characterize existence and structural properties for (globally) optimal policies. We consider in particular both static and dynamic non-convex team problems where the cost function and dynamics satisfy an exchangeability condition. We first establish a de Finetti type representation theorem for exchangeable decentralized policies, that is, for the probability measures induced by admissible policies under decentralized information structures. For a general setup of stochastic team problems with N decision makers, under exchangeability of observations of decision makers and the cost function, we show that without loss of global optimality, the search for optimal policies over any convex set of probability measures on policies can be restricted to those that are N-exchangeable. Then, by extending N-exchangeable policies to infinitely exchangeable ones, establishing a convergence argument for the induced costs, and using the presented de Finetti type theorem, we establish the existence of an optimal decentralized policy for static and dynamic teams with countably infinite number of decision makers, which turns out to be symmetric (i.e., identical) and randomized. In particular, unlike prior work, convexity of the cost is not assumed.
DOI	10.1109/CDC42340.2020.9304328

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Independently randomized symmetric policies are optimal for exchangeable stochastic teams with infinitely many decision makers

Yazar Sanjari, S., Saldı, Naci, Yüksel, S.

Basım Tarihi 2020-12-14

Basım Yeri - IEEE

Tür Belge

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0743-1546

Kayıt Numarası 8d9e719f-01d7-44f2-b0b1-066ea0a4a11d

Lokasyon Natural and Mathematical Sciences

Tarih 2020-12-14

Notlar Natural Sciences and Engineering Research Council (NSERC) of Canada

Örnek Metin We study stochastic team (known also as decentralized stochastic control or identical interest stochastic game) problems with large or countably infinite number of decision makers, and characterize existence and structural properties for (globally) optimal policies. We consider in particular both static and dynamic non-convex team problems where the cost function and dynamics satisfy an exchangeability condition. We first establish a de Finetti type representation theorem for exchangeable decentralized policies, that is, for the probability measures induced by admissible policies under decentralized information structures. For a general setup of stochastic team problems with N decision makers, under exchangeability of observations of decision makers and the cost function, we show that without loss of global optimality, the search for optimal policies over any convex set of probability measures on policies can be restricted to those that are N-exchangeable. Then, by extending N-exchangeable policies to infinitely exchangeable ones, establishing a convergence argument for the induced costs, and using the presented de Finetti type theorem, we establish the existence of an optimal decentralized policy for static and dynamic teams with countably infinite number of decision makers, which turns out to be symmetric (i.e., identical) and randomized. In particular, unlike prior work, convexity of the cost is not assumed.

DOI 10.1109/CDC42340.2020.9304328