  We consider the problem of finitely parameterized multi-armed bandits where
the model of the underlying stochastic environment can be characterized based
on a common unknown parameter. The true parameter is unknown to the learning
agent. However, the set of possible parameters, which is finite, is known a
priori. We propose an algorithm that is simple and easy to implement, which we
call Finitely Parameterized Upper Confidence Bound (FP-UCB) algorithm, which
uses the information about the underlying parameter set for faster learning. In
particular, we show that the FP-UCB algorithm achieves a bounded regret under
some structural condition on the underlying parameter set. We also show that,
if the underlying parameter set does not satisfy the necessary structural
condition, the FP-UCB algorithm achieves a logarithmic regret, but with a
smaller preceding constant compared to the standard UCB algorithm. We also
validate the superior performance of the FP-UCB algorithm through extensive
numerical simulations.
