  In the multiarmed bandit problem a gambler chooses an arm of a slot machine
to pull considering a tradeoff between exploration and exploitation. We study
the stochastic bandit problem where each arm has a reward distribution
supported in a known bounded interval, e.g. [0,1]. For this model, policies
which take into account the empirical variances (i.e. second moments) of the
arms are known to perform effectively. In this paper, we generalize this idea
and we propose a policy which exploits the first d empirical moments for
arbitrary d fixed in advance. The asymptotic upper bound of the regret of the
policy approaches the theoretical bound by Burnetas and Katehakis as d
increases. By choosing appropriate d, the proposed policy realizes a tradeoff
between the computational complexity and the expected regret.
