Linearly parameterized bandits
Name
P-09-linearBandit-fin.pdf
Size
311.53 KB
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Adobe PDF
Checksum (MD5)
5464e7b654c5e7e25cb445f091892fe5
Author(s)
Tsitsiklis, John N.
Rusmevichientong, Paat
Date Issued
January 2010
Journal
Mathematics of Operations Research
Publisher
INFORMS
Citation
Rusmevichientong, P., and J. N. Tsitsiklis. “Linearly Parameterized Bandits.” Mathematics of Operations Research 35.2 (2010): 395-411.
Version
Author's final manuscript
Abstract
We consider bandit problems involving a large (possibly infinite) collection of arms, in which the expected reward of each arm is a linear function of an r-dimensional random vector Z ∈ ℝ(superscript r), where r ≥ 2. The objective is to minimize the cumulative regret and Bayes risk. When the set of arms corresponds to the unit sphere, we prove that the regret and Bayes risk is of order Θ(r √T), by establishing a lower bound for an arbitrary policy, and showing that a matching upper bound is obtained through a policy that alternates between exploration and exploitation phases. The phase-based policy is also shown to be effective if the set of arms satisfies a strong convexity condition. For the case of a general set of arms, we describe a near-optimal policy whose regret and Bayes risk admit upper bounds of the form O(r √T log(superscript 3/2)T).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1287/moor.1100.0446
