Online decision problems with large strategy sets
Name
62173704-MIT.pdf
Description
Full printable version
Size
9.6 MB
Format
Adobe PDF
Checksum (MD5)
844518d3bfb3c93741973aa7c68389e3
Author(s)
Kleinberg, Robert David
Advisor(s)
F. Thomson Leighton.
Date Issued
2005
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 165-171).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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