NDLI: Stochastic Nestedness and the Belief Sharing Information Pattern

Content Provider	IEEE Xplore Digital Library
Author	Yuksel, S.
Copyright Year	1963
Abstract	Solutions to decentralized stochastic optimization problems lead to recursions in which the state space enlarges with the time-horizon, thus leading to non-tractability of classical dynamic programming. A common joint information state supplied to each of the agents leads to a tractable recursion, as is evident in the one-step-delayed information sharing structure case or when deterministic nestedness in information holds when there is a causality relationship as in the case of partially nested information structure. However, communication requirements for such conditions require exchange of very large data noiselessly, hence these assumptions are generally impractical. In this paper, we present a weaker notion of nestedness, which we term as stochastic nestedness, which is characterized by a sequence of Markov chain conditions. It is shown that if the information structure is stochastically nested, then an optimization problem is tractable, and in particular for LQG problems, the team optimal solution is linear, despite the lack of deterministic nestedness or partial nestedness. One other contribution of this paper is that, by regarding the multiple decision makers as a single decision maker and using Witsenhausen's equivalent model for discrete-stochastic control, it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions; a pattern we refer to as k-stage belief sharing pattern. We discuss the minimum amount of information exchange required to achieve such an information pattern for k =1. The information exchange needed is generally strictly less than what is needed for deterministic nestedness and is zero whenever stochastic nestedness applies. In view of nestedness, we present a discussion on the monotone values of information channels.
Sponsorship	IEEE Control Systems Society
Starting Page	2773
Ending Page	2786
Page Count	14
File Size	378863
File Format	PDF
ISSN	00189286
Volume Number	54
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stochastic processes Distributed control Communication system control Mathematics Automatic generation control Associate members State-space methods Dynamic programming Stochastic resonance Decision theory team decision theory Communication complexity decentralized control information-control structure (ICS) stochastic control
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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