Four proofs of Gittins’ multiarmed bandit theorem

Esther Frostig () and Gideon Weiss ()
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Esther Frostig: The University of Haifa
Gideon Weiss: The University of Haifa

Annals of Operations Research, 2016, vol. 241, issue 1, No 8, 127-165

Abstract: Abstract We study four proofs that the Gittins index priority rule is optimal for alternative bandit processes. These include Gittins’ original exchange argument, Weber’s prevailing charge argument, Whittle’s Lagrangian dual approach, and Bertsimas and Niño-Mora’s proof based on the achievable region approach and generalized conservation laws. We extend the achievable region proof to infinite countable state spaces, by using infinite dimensional linear programming theory.

Keywords: Dynamic programming; Bandit problems; Gittins index; Linear programming (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10479-013-1523-0

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