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Bounded regret in stochastic multi-armed bandits
- JMLR: WORKSHOP AND CONFERENCE PROCEEDINGS VOL (2013) 1–13
, 2013
"... We study the stochastic multi-armed bandit problem when one knows the valueµ (⋆) of an optimal arm, as a well as a positive lower bound on the smallest positive gap∆. We propose a new randomized policy that attains a regret uniformly bounded over time in this setting. We also prove several lower bou ..."
Abstract
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Cited by 5 (2 self)
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We study the stochastic multi-armed bandit problem when one knows the valueµ (⋆) of an optimal arm, as a well as a positive lower bound on the smallest positive gap∆. We propose a new randomized policy that attains a regret uniformly bounded over time in this setting. We also prove several lower bounds, which show in particular that bounded regret is not possible if one only knows ∆, and bounded regret of order1/ ∆ is not possible if one only knowsµ (⋆).
The best of both worlds: Stochastic and adversarial bandits.
- In COLT,
, 2012
"... Abstract We present a new bandit algorithm, SAO (Stochastic and Adversarial Optimal) whose regret is (essentially) optimal both for adversarial rewards and for stochastic rewards. Specifically, SAO combines the O( √ n) worst-case regret of Exp3 ..."
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Cited by 4 (0 self)
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Abstract We present a new bandit algorithm, SAO (Stochastic and Adversarial Optimal) whose regret is (essentially) optimal both for adversarial rewards and for stochastic rewards. Specifically, SAO combines the O( √ n) worst-case regret of Exp3
ONLINE LEARNING AND GAME THEORY. A QUICK OVERVIEW WITH RECENT RESULTS AND APPLICATIONS
, 2015
"... We study one of the main concept of online learning and sequential decision problem known as regret minimization. We investigate three different frameworks, whether data are generated accordingly to some i.i.d. process, or when no assumption whatsoever are made on their generation and, finally, whe ..."
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We study one of the main concept of online learning and sequential decision problem known as regret minimization. We investigate three different frameworks, whether data are generated accordingly to some i.i.d. process, or when no assumption whatsoever are made on their generation and, finally, when they are the consequences of some sequential interactions between players. The overall objective is to provide a comprehensive introduction to this domain. In each of these main setups, we define and analyze classical algorithms and we analyze their performances. Finally, we also show that some concepts of equilibria that emerged in game theory are learnable by players using online learning schemes while some other concepts are not learnable.
25th Annual Conference on Learning Theory The Best of Both Worlds: Stochastic and Adversarial Bandits
"... We present a new bandit algorithm, SAO (Stochastic and Adversarial Optimal) whose regret is (essentially) optimal both for adversarial rewards and for stochastic rewards. Specifically, SAO combines the O ( √ n) worst-case regret of Exp3 (Auer et al., 2002b) and the (poly)logarithmic regret of UCB1 ..."
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We present a new bandit algorithm, SAO (Stochastic and Adversarial Optimal) whose regret is (essentially) optimal both for adversarial rewards and for stochastic rewards. Specifically, SAO combines the O ( √ n) worst-case regret of Exp3 (Auer et al., 2002b) and the (poly)logarithmic regret of UCB1 (Auer et al., 2002a) for stochastic rewards. Adversarial rewards and stochastic rewards are the two main settings in the literature on multi-armed bandits (MAB). Prior work on MAB treats them separately, and does not attempt to jointly optimize for both. This result falls into the general agenda to design algorithms that combine the optimal worst-case performance with improved guarantees for “nice ” problem instances. 1.
