Four proofs of Gittins’ multiarmed bandit theorem

Esther Frostig; Gideon Weiss

doi:10.1007/s10479-013-1523-0

Four proofs of Gittins’ multiarmed bandit theorem

Esther Frostig, Gideon Weiss

Department of Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	127-165
Number of pages	39
Journal	Annals of Operations Research
Volume	241
Issue number	1-2
DOIs	https://doi.org/10.1007/s10479-013-1523-0
State	Published - 1 Jun 2016

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Keywords

Bandit problems
Dynamic programming
Gittins index
Linear programming

ASJC Scopus subject areas

General Decision Sciences
Management Science and Operations Research

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10.1007/s10479-013-1523-0

Cite this

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abstract = "We study four proofs that the Gittins index priority rule is optimal for alternative bandit processes. These include Gittins{\textquoteright} original exchange argument, Weber{\textquoteright}s prevailing charge argument, Whittle{\textquoteright}s Lagrangian dual approach, and Bertsimas and Ni{\~n}o-Mora{\textquoteright}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.",

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Four proofs of Gittins’ multiarmed bandit theorem

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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