We are interested in the problem of utilizing collected data to inform and direct learning towards a stated goal. In this work, a controller is presented with a finite set of actions that may be sequentially (and repeatedly) taken towards the achievement of some goal. While the outcome of any action is stochastic, the result provides information about future results of that action, and potentially others. By following a rule or control policy, the controller wishes to sequentially take actions, collect information, and utilize it towards future action decisions, in such a way as to approach the stated goal. In the first model, at least one action is `best', and the goal is to identify and take such an action as frequently as possible. This requires learning the actions' underlying dynamics based on repeated observations of the stochastic results of those actions; this encapsulates the classic `exploration vs exploitation' dynamic, to test many actions, or to take only the action currently believed to be best. We derive asymptotic lower bounds on how effective any universally good policy can be, as a function of initial knowledge. Additionally, we define a generic control policy and conditions under which it is provably asymptotically optimal, and give a number of examples to illustrate the scope and application of the model. In the second model, the goal is to maximize some utility of all actions taken, e.g., total expected rewards collected. Additionally, each action has an associated breaking or halting time, which if reached ends the control process. This again captures the `exploration vs exploitation' dynamic, as the controller must balance the reward of any one action against the risk of halting and loss of opportunity for future rewards. As the goal depends on the actual results achieved, there is generally no single `best' action as in the previous model. In many contexts, we derive a dynamic `action valuation' scheme that gives rise to an optimal control policy.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_7261
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (viii, 89 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Charles Wesley Cowan
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.