Author
Sanjari, S., Saldı, Naci, Yüksel, S.
Publication Date
2020-12-14
Publication Place
-
IEEE
Type
Document
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
0743-1546
Record ID
8d9e719f-01d7-44f2-b0b1-066ea0a4a11d
Library Location
Natural and Mathematical Sciences
Date
2020-12-14
Notes
Natural Sciences and Engineering Research Council (NSERC) of Canada
Sample Text
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
