Multi-armed Bandits with Constrained Arms and Hidden States

The problem of rested and restless multi-armed bandits with constrained availability of arms is considered. The states of arms evolve in Markovian manner and the exact states are hidden from the decision maker. First, some structural results on value functions are claimed. Following these results, the optimal policy turns out to be a $\mathit{\text{threshold}}\mathit{\text{policy}}$. Further, $\mathit{\text{indexability}}$ of rested bandits is established and index formula is derived. The performance of index policy is illustrated and compared with myopic policy using numerical examples.