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Four proofs of Gittins’ multiarmed bandit theorem

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Listed:
  • Esther Frostig

    (The University of Haifa)

  • Gideon Weiss

    (The University of Haifa)

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.

Suggested Citation

  • Esther Frostig & Gideon Weiss, 2016. "Four proofs of Gittins’ multiarmed bandit theorem," Annals of Operations Research, Springer, vol. 241(1), pages 127-165, June.
    • Handle: RePEc:spr:annopr:v:241:y:2016:i:1:d:10.1007_s10479-013-1523-0
    DOI: 10.1007/s10479-013-1523-0
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    Cited by:

    1. Samuel N. Cohen & Tanut Treetanthiploet, 2019. "Gittins' theorem under uncertainty," Papers 1907.05689, arXiv.org, revised Jun 2021.
    2. Francisco Alvarez, 2018. "Decomposing risk in an exploitation–exploration problem with endogenous termination time," Annals of Operations Research, Springer, vol. 261(1), pages 45-77, February.

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