  We consider restless multi-armed bandit (RMAB) with a finite horizon and
multiple pulls per period. Leveraging the Lagrangian relaxation, we approximate
the problem with a collection of single arm problems. We then propose an
index-based policy that uses optimal solutions of the single arm problems to
index individual arms, and offer a proof that it is asymptotically optimal as
the number of arms tends to infinity. We also use simulation to show that this
index-based policy performs better than the state-of-art heuristics in various
problem settings.
