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The stochastic multi-armed bandit problem is well understood when the reward distributions are sub-Gaussian.
Some aspects of the sequential design of experiments
H. Robbins · 1952
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Robust estimation of a location parameter
P. J. Huber · 1964
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On some robust estimates of location
P. J. Bickel · 1965
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Robust Statistics
P. J. Huber · 1981
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Asymptotically efficient adaptive allocation rules
T. L. Lai and H. Robbins · 1985
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Sample mean based index policies with O ( log n ) {O}(\log n) regret for the multi-armed bandit problem
R. Agrawal · 1995
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The racing algorithm: Model selection for lazy learners
O. Maron and A.W. Moore · 1997
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An optimal algorithm for monte carlo estimation
P. Dagum, R. Karp, M. Luby, and S. Ross · 2000
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The space complexity of approximating the frequency moments
N. Alon, Y. Matias, and M. Szegedy · 2002
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Finite-time analysis of the multiarmed bandit problem
P. Auer, N. Cesa-Bianchi, and P. Fischer · 2002
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Adaptive sampling methods for scaling up knowledge discovery algorithms
C. Domingo, R. Gavaldà, and O. Watanabe · 2002
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Bandits Games and Clustering Foundations
S. Bubeck · 2010
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Challenging the empirical mean and empirical variance: a deviation study
O. Catoni · 2010
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The KL-UCB algorithm for bounded stochastic bandits and beyond
A. Garivier and O. Cappé · 2011
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Deterministic Sequencing of Exploration and Exploitation for Multi-Armed Bandit Problems
K. Liu and Q. Zhao · 2011
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Regret analysis of stochastic and nonstochastic multi-armed bandit problems
S. Bubeck and N. Cesa-Bianchi · 2012
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