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A Short Proof of the Gittins Index Theorem
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We provide a short and elementary proof of the Gittins index theorem for the multi-armed bandit problem, for the case where each bandit is modeled as a finite-state semi-Markov process. We also indicate how this proof can be extended to the branching bandits and Klimov problems.
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“Although it could be argued that participants should explore in this task and therefore that referencing choices to an ideal observer is not optimal, exploration should be minimized to perform optimally, as we used stationary distributions and therefore this is a 2-armed bandit task (Tsitsiklis, 1994).”
From Oxytocin decreases aversion to angry faces in an associative learning task (2010) · cites this paper as Tsitsiklis, 1994
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Research works printed but not linked: 4
- [2][2] GITTINs, J. C. (1989). Multi-Armed Bandit Allocation Indices. Wiley, New York. -
- [3][3] GITTINS, J. C. and JoNEs, D. M. (1974). A dynamic allocation index for the design of experiments. In Progress in Statistics (J. Gani, K. Sarkadi and I. Vince, eds.) Colloq. Math. Soc. János Bolyai 9. North-Holland, Amsterdam. -
- [7][7] TsITsIKLIs, J. N. (1986). A lemma on the multi-armed bandit problem. IEEE Trans. Automat. Control 31 576–577. -
- [9][9] VARAIYA, P., WALRAND, J. and BUYUKKOC, C. (1985). Extensions of the multi-armed bandit problem: The discounted case. IEEE Trans. Automat. Control AC-30 426-439. -
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Metadata
- Authors
- Tsitsiklis, J. N.
- Corresponding author
- Tsitsiklis, John N.
- ORCID
- Tsitsiklis, John N.
- Venue
- The Annals of Applied Probability
- Publisher
- Institute of Mathematical Statistics
- Published
- 1994-02-01
- Volume
- 4
- Issue
- 1
- Pages
- 194-199
- ISSN
- 1050-5164 (ISSN-L)
- 2168-8737
- OpenAlex
- W2159471113
- Cited by
- 143
- References
- 0
- Citations by year
- 2025: 3 · 2024: 1 · 2023: 2 · 2022: 2 · 2021: 1 · 2020: 54 · 2019: 6 · 2018: 2 · 2017: 1 · 2016: 5 · 2015: 3 · 2014: 5 · 2013: 7 · 2012: 5
- FWCI
- 2.76
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Applied Probability (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Advanced Bandit Algorithms Research
- Physical Sciences › Mathematics › Theoretical Computer Science › Optimization and Search Problems
- Social Sciences › Decision Sciences › Management Science and Operations Research › Game Theory and Applications
- Keywords
- multi-armed bandits, optimal stopping, sequential decision making
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