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We analyze the minimax regret of the adversarial bandit convex optimization problem.
On general minimax theorems
M. Sion · 1958
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On the likelihood that one unknown probability exceeds another in view of the evidence of two samples
W. Thompson · 1958
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Mixed and behavior strategies in infinite extensive games
R. J. Aumann · 1964
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Elementary proof for Sion’s minimax theorem
H. Komiya · 1988
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Exponentiated gradient versus gradient descent for linear predictors
J. Kivinen and M. K. Warmuth · 1997
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The non-stochastic multi-armed bandit problem
P. Auer, N. Cesa-Bianchi, Y. Freund, and R. Schapire · 2002
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Nearly tight bounds for the continuum-armed bandit problem
R. Kleinberg · 2004
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Online convex optimization in the bandit setting: Gradient descent without a gradient
A. Flaxman, A. Kalai, and B. McMahan · 2005
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Competing in the dark: An efficient algorithm for bandit linear optimization
J. Abernethy, E. Hazan, and A. Rakhlin · 2008
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The price of bandit information for online optimization
V. Dani, T. Hayes, and S. Kakade · 2008
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A stochastic view of optimal regret through minimax duality
J. Abernethy, A. Agarwal, P. Bartlett, and A. Rakhlin · 2009
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Optimal algorithms for online convex optimization with multi-point bandit feedback
A. Agarwal, O. Dekel, and L. Xiao · 2010
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Stochastic convex optimization with bandit feedback
A. Agarwal, D. Foster, D. Hsu, S. Kakade, and A. Rakhlin · 2011
Improved regret guarantees for online smooth convex optimization with bandit feedback
A. Saha and A. Tewari · 2011
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Towards minimax policies for online linear optimization with bandit feedback
S. Bubeck, N. Cesa-Bianchi, and S. Kakade · 2012
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The maximal variation of martingales of probabilities and repeated games with incomplete information
A. Neyman · 2013
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Towards optimal algorithms for prediction with expert advice
N. Gravin, Y. Peres, and B. Sivan · 2014
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Bandit convex optimization: Towards tight bounds
E. Hazan and K. Levy · 2014
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D. Russo and B. van Roy · 2014
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