國立虎尾科技大學 |

Decision and learning in large networks.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Decision and learning in large networks./
作者:	Zhang, Zhenliang.
面頁冊數:	1 online resource (214 pages)
附註:	Source: Dissertations Abstracts International, Volume: 75-08, Section: B.
Contained By:	Dissertations Abstracts International75-08B.
標題:	Social research. -
電子資源:	click for full text (PQDT)
ISBN:	9781303667039

Decision and learning in large networks.
Zhang, Zhenliang.

Decision and learning in large networks. - 1 online resource (214 pages)

Source: Dissertations Abstracts International, Volume: 75-08, Section: B.

Thesis (Ph.D.)--Colorado State University, 2013.

Includes bibliographical references

We consider two topics in this thesis: 1) learning in feedforward and hierarchical networks; and 2) string submodularity in optimal control problems. In the first topic, we consider a binary hypothesis testing problem and an associated network that attempts jointly to solve the problem. Each agent in the network takes a private signal of the underlying truth, observes the past actions of his neighboring agents, and makes a decision to optimize an objective function (e.g., probability of error). We are interested in the following questions: 1) Will the agents asymptotically learn the underlying truth? More specifically, will the overall decision converges (in probability) to the underlying truth as the number of agents goes to infinity? 2) If so, how fast is the convergence with respect to the number of agents? To answer these questions, we investigate two types of networks: Feedforward network and hierarchical tree network, which arise naturally in social and technological networks. Moreover, we investigate the following three parameters: 1. memory size; 2. private signal `strength;' 3. communication noisiness. We establish conditions on these parameters such that the agents asymptotically learn the underlying truth. Moreover, we study the relationship between the convergence rates and these parameters. First, we consider the feedforward network, consisting of a large number of nodes, which sequentially make decisions between two given hypotheses. Each node takes a private signal of the underlying truth, observes the decisions from some immediate predecessors, and makes a decision between the given hypotheses. Second, we consider the hypothesis testing problem in the context of balanced binary relay trees, where the leaves (and only the leaves) of the tree correspond to N identical and independent sensors. The root of the tree represents a fusion center that makes the overall decision. Each of the other nodes in the tree is a relay node that combines two binary messages to form a single output binary message. In this way, the information from the sensors is aggregated into the fusion center via the relay nodes. In the second topic, we extend the notion of submodularity to optimal control problems. More precisely, we introduce the notion of string submodularity in the problem of maximizing an objective function defined on a set of strings subject to a string length constraint. We show that the greedy strategy achieves a (1-e-1)-approximation of the optimal strategy. Moreover, we can improve this approximation by introducing additional constraints on curvature, namely, total backward curvature, total forward curvature, and elemental forward curvature. We also introduce the notion of string-matroid and consider the problem of maximizing the objective function subject to a string-matroid constraint. We investigate three applications of string submodular functions with curvature constraints: 1) designing a string of fusion rules in balanced binary relay trees such that the reduction in the error probability is maximized; 2) choosing a string of actions to maximize the expected fraction of accomplished tasks; and 3) designing a string of measurement matrices such that the information gain is maximized. (Abstract shortened by UMI.).

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9781303667039Subjects--Topical Terms:

1179269
Social research.
Subjects--Index Terms:

Bayesian learningIndex Terms--Genre/Form:

554714
Electronic books.

Decision and learning in large networks.
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504 $a Includes bibliographical references
520 $a We consider two topics in this thesis: 1) learning in feedforward and hierarchical networks; and 2) string submodularity in optimal control problems. In the first topic, we consider a binary hypothesis testing problem and an associated network that attempts jointly to solve the problem. Each agent in the network takes a private signal of the underlying truth, observes the past actions of his neighboring agents, and makes a decision to optimize an objective function (e.g., probability of error). We are interested in the following questions: 1) Will the agents asymptotically learn the underlying truth? More specifically, will the overall decision converges (in probability) to the underlying truth as the number of agents goes to infinity? 2) If so, how fast is the convergence with respect to the number of agents? To answer these questions, we investigate two types of networks: Feedforward network and hierarchical tree network, which arise naturally in social and technological networks. Moreover, we investigate the following three parameters: 1. memory size; 2. private signal `strength;' 3. communication noisiness. We establish conditions on these parameters such that the agents asymptotically learn the underlying truth. Moreover, we study the relationship between the convergence rates and these parameters. First, we consider the feedforward network, consisting of a large number of nodes, which sequentially make decisions between two given hypotheses. Each node takes a private signal of the underlying truth, observes the decisions from some immediate predecessors, and makes a decision between the given hypotheses. Second, we consider the hypothesis testing problem in the context of balanced binary relay trees, where the leaves (and only the leaves) of the tree correspond to N identical and independent sensors. The root of the tree represents a fusion center that makes the overall decision. Each of the other nodes in the tree is a relay node that combines two binary messages to form a single output binary message. In this way, the information from the sensors is aggregated into the fusion center via the relay nodes. In the second topic, we extend the notion of submodularity to optimal control problems. More precisely, we introduce the notion of string submodularity in the problem of maximizing an objective function defined on a set of strings subject to a string length constraint. We show that the greedy strategy achieves a (1-e-1)-approximation of the optimal strategy. Moreover, we can improve this approximation by introducing additional constraints on curvature, namely, total backward curvature, total forward curvature, and elemental forward curvature. We also introduce the notion of string-matroid and consider the problem of maximizing the objective function subject to a string-matroid constraint. We investigate three applications of string submodular functions with curvature constraints: 1) designing a string of fusion rules in balanced binary relay trees such that the reduction in the error probability is maximized; 2) choosing a string of actions to maximize the expected fraction of accomplished tasks; and 3) designing a string of measurement matrices such that the information gain is maximized. (Abstract shortened by UMI.).
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