Multi-armed Bandits with Constrained Arms and Hidden States
For decision makers in resource-constrained environments with hidden state evolution, this work provides a tractable index policy, though the results are incremental extensions of existing bandit theory.
The paper addresses multi-armed bandits with constrained arms and hidden Markovian states, establishing indexability for rested bandits and deriving an index formula. Numerical examples show the index policy outperforms the myopic policy.
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 \textit{threshold policy}. Further, \textit{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.