Finite-time Regret Bound of a Bandit Algorithm for the Semi-bounded Support Model

Junya Honda; Akimichi Takemura

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arXiv · 1202.2277

Finite-time Regret Bound of a Bandit Algorithm for the Semi-bounded Support Model

Junya Honda·Akimichi Takemura

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Abstract

In this paper we consider stochastic multiarmed bandit problems. Recently a policy, DMED, is proposed and proved to achieve the asymptotic bound for the model that each reward distribution is supported in a known bounded interval, e.g. [0,1]. However, the derived regret bound is described in an asymptotic form and the performance in finite time has been unknown. We inspect this policy and derive a finite-time regret bound by refining large deviation probabilities to a simple finite form. Further, this observation reveals that the assumption on the lower-boundedness of the support is not essential and can be replaced with a weaker one, the existence of the moment generating function.

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Junya Honda, Akimichi Takemura. 2012-02-10. Finite-time Regret Bound of a Bandit Algorithm for the Semi-bounded Support Model. https://arxiv.org/abs/1202.2277

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