The DOI matches its Crossref record.
A Short Proof of the Gittins Index Theorem
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
The publisher hasn’t deposited this paper’s reference list.
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. -
Cited by
Sorted by citations
Items 101–146 of 146
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.015
The Upper Confidence Bound Algorithm: Minimax Optimality
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.012
Stochastic Processes and Markov Chains
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.005
Confidence Bounds for Least Squares Estimators
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.026 · Cited by 1
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.023
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.018
The Upper Confidence Bound Algorithm: Asymptotic Optimality
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.011
A perpetual search for talents across overlapping generations: A learning process
Agbo, M. (2015) · Mathematical Social Sciences · doi:10.1016/j.mathsocsci.2015.05.002
Stochastic Linear Bandits with Finitely Many Arms
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.028
Optimal Design for Least Squares Estimators
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.027
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.047
Bandits, Probability and Concentration
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.002
The Upper Confidence Bound Algorithm: Bernoulli Noise
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.013
Exp3 for Adversarial Linear Bandits
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.034
Foundations of Bayesian Learning
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.042
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.025
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.032
Gittins, J. C., Glazebrook, K. D., & Weber, R. (2011) · doi:10.1002/9780470980033.refs
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.020
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.039
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.037
Adversarial Bandits with Finitely Many Arms
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.014
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.041
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.006 · Cited by 1
Asymptotic Lower Bounds for Stochastic Linear Bandits
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.031
Lower Bounds for Bandits with Finitely Many Arms
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.017
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.048
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.045
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.046 · Cited by 1
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.001
Minimax Lower Bounds for Stochastic Linear Bandits
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.030
Stochastic Linear Bandits with Sparsity
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.029
The Relation between Adversarial and Stochastic Linear Bandits
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.036
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.022
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.043
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.007
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.004
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.040
Follow-the-regularised-Leader and Mirror Descent
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.035 · Cited by 1
Instance-Dependent Lower Bounds
Lattimore, T., & Szepesvári, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108571401.021 · Cited by 1
Zacks, S. (2008) · Wiley series in probability and statistics · doi:10.1002/9780470466957.biblio
On the undiscounted tax problem with precedence constraints
Glazebrook, K. D. (1996) · Advances in Applied Probability · doi:10.1017/s0001867800027580
Wu, Q. (2022) · Operations Research Letters · doi:10.1016/j.orl.2022.09.002
Niño‐Mora, J. (2024) · Encyclopedia of Optimization · doi:10.1007/978-3-030-54621-2_665-1
Online Learning in Bandit Problems.
Tekin, C. (2013) · Deep Blue (University of Michigan)
Bandit feedback in Classification and Multi-objective Optimization
Zhong, H. (2016) · theses.fr (ABES) · doi:10.70675/ee120338z32b2z4f86za36dzec2dec8cc01b
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
