2026-09-20T21:01:42Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/330922022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
F. Thomson Leighton.
Kleinberg, Robert David
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-06-19T17:39:44Z
2006-06-19T17:39:44Z
2005
2005
http://hdl.handle.net/1721.1/33092
62173704
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 165-171).
In an online decision problem, an algorithm performs a sequence of trials, each of which involves selecting one element from a fixed set of alternatives (the "strategy set") whose costs vary over time. After T trials, the combined cost of the algorithm's choices is compared with that of the single strategy whose combined cost is minimum. Their difference is called regret, and one seeks algorithms which are efficient in that their regret is sublinear in T and polynomial in the problem size. We study an important class of online decision problems called generalized multi- armed bandit problems. In the past such problems have found applications in areas as diverse as statistics, computer science, economic theory, and medical decision-making. Most existing algorithms were efficient only in the case of a small (i.e. polynomial- sized) strategy set. We extend the theory by supplying non-trivial algorithms and lower bounds for cases in which the strategy set is much larger (exponential or infinite) and the cost function class is structured, e.g. by constraining the cost functions to be linear or convex. As applications, we consider adaptive routing in networks, adaptive pricing in electronic markets, and collaborative decision-making by untrusting peers in a dynamic environment.
by Robert David Kleinberg.
Ph.D.
171 p.
10061360 bytes
10071115 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Online decision problems with large strategy sets
Thesis
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