Finite dimensional algorithms for the hidden Markov model multi-armed bandit problem

The multi-arm bandit problem is widely used in scheduling of traffic in broadband networks, manufacturing systems and robotics. This paper presents a finite dimensional optimal solution to the multi-arm bandit problem for Hidden Markov Models. The key to solving any multi-arm bandit problem is to compute the Gittins index. In this paper a finite dimensional algorithm is presented which exactly computes the Gittins index. Suboptimal algorithms for computing the Gittins index are also presented and experimentally shown to perform almost as well as the optimal method. Finally an application of the algorithms to tracking multiple targets with a single intelligent sensor is presented.