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We present methods for online linear optimization that take advantage of benign (as opposed to worst-case) sequences.
The nonstochastic multiarmed bandit problem
P. Auer, N. Cesa-Bianchi, Y. Freund, and R. E. Schapire · 2003
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Mirror descent and nonlinear projected subgradient methods for convex optimization
A. Beck and M. Teboulle · 2003
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Efficient algorithms for online decision problems
A. Kalai and S. Vempala · 2005
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Prediction, Learning, and Games
N. Cesa-Bianchi and G. Lugosi · 2006
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Adaptive online gradient descent
P.L. Bartlett, E. Hazan, and A. Rakhlin · 2007
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Improved second-order bounds for prediction with expert advice
N. Cesa-Bianchi, Y. Mansour, and G. Stoltz · 2007
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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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Interior-point methods for optimization
A.S. Nemirovski and M.J. Todd · 2008
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Lecture notes on online learning, 2008
A. Rakhlin · 2008
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Beating the adaptive bandit with high probability
J. Abernethy and A. Rakhlin · 2009
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Better algorithms for benign bandits
E. Hazan and S. Kale · 2009
Cited alongside, same era.
Extracting certainty from uncertainty: Regret bounded by variation in costs
E. Hazan and S. Kale · 2010
Cited alongside, same era.
Online learning: Random averages, combinatorial parameters, and learnability
A. Rakhlin, K. Sridharan, and A. Tewari · 2010
Later among the works it cites.
Online learning: Stochastic, constrained, and smoothed adversaries
A. Rakhlin, K. Sridharan, and A. Tewari · 2011
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Interior-point methods for full-information and bandit online learning
J.D. Abernethy, E. Hazan, and A. Rakhlin · 2012
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Online optimization with gradual variations
C.-K. Chiang, T. Yang, C.-J. Lee, M. Mahdavi, C.-J. Lu, R. Jin, and S. Zhu · 2012
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Relax and localize: From value to algorithms
A. Rakhlin, O. Shamir, and K. Sridharan · 2012
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