Perseus: Randomized Point-based Value Iteration for POMDPs
  Partially observable Markov decision processes (POMDPs) form an attractive
and principled framework for agent planning under uncertainty. Point-based
approximate techniques for POMDPs compute a policy based on a finite set of
points collected in advance from the agents belief space. We present a
randomized point-based value iteration algorithm called Perseus. The algorithm
performs approximate value backup stages, ensuring that in each backup stage
the value of each point in the belief set is improved; the key observation is
that a single backup may improve the value of many belief points. Contrary to
other point-based methods, Perseus backs up only a (randomly selected) subset
of points in the belief set, sufficient for improving the value of each belief
point in the set. We show how the same idea can be extended to dealing with
continuous action spaces. Experimental results show the potential of Perseus in
large scale POMDP problems.
