  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.
