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In (online) learning theory the concepts of sparsity, variance and curvature are well-understood and are routinely used to obtain refined regret and generalization bounds.
Interior-point polynomial algorithms in convex programming
Y. Nesterov and A. Nemirovski · 1994
Earlier work this paper cites.
The non-stochastic multi-armed bandit problem
P. Auer, N. Cesa-Bianchi, Y. Freund, and R. Schapire · 2002
Earlier work this paper cites.
Competing in the dark: An efficient algorithm for bandit linear optimization
J. Abernethy, E. Hazan, and A. Rakhlin · 2008
Earlier work this paper cites.
Minimax policies for adversarial and stochastic bandits
J.-Y. Audibert and S. Bubeck · 2009
Earlier work this paper cites.
Better algorithms for benign bandits
E. Hazan and S. Kale · 2009
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Sparse online learning via truncated gradient
J. Langford, L. Li, and T. Zhang · 2009
Earlier work this paper cites.
A simple multi-armed bandit algorithm with optimal variation-bounded regret
E. Hazan and S. Kale · 2011
Cited alongside, same era.
Regret analysis of stochastic and nonstochastic multi-armed bandit problems
S. Bubeck and N. Cesa-Bianchi · 2012
Cited alongside, same era.
Towards minimax policies for online linear optimization with bandit feedback
S. Bubeck, N. Cesa-Bianchi, and S.M. Kakade · 2012
Cited alongside, same era.
Regret in online combinatorial optimization
J.Y. Audibert, S. Bubeck, and G. Lugosi · 2014
Cited alongside, same era.
Bandit convex optimization: Towards tight bounds
E. Hazan and K. Levy · 2014
Cited alongside, same era.
Efficient learning by implicit exploration in bandit problems with side observations
T. Kocák, G. Neu, M. Valko, and R. Munos · 2014
Cited alongside, same era.
Convex optimization: Algorithms and complexity
S. Bubeck · 2015
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Explore no more: Improved high-probability regret bounds for non-stochastic bandits
G. Neu · 2015
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Learning in games: Robustness of fast convergence
D. Foster, Z. Li, T. Lykouris, K. Sridharan, and E. Tardos · 2016
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Refined lower bounds for adversarial bandits
S. Gerchinovitz and T. Lattimore · 2016
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Gains and losses are fundamentally different in regret minimization: The sparse case
J. Kwon and V. Perchet · 2016
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