Bounded Regret for Finitely Parameterized Multi-Armed Bandits

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