Value Iteration Working With Belief Subsets

Value iteration is a popular algorithm for solving POMDPs. However, it is inefficient in practice. The primary reason is that it needs to conduct value updates for all the belief states in the (continuous) belief space. In this paper, we study value iteration working with a subset of the belief space, i.e., it conducts value updates only for belief states in the subset. We present a way to select belief subset and describe an algorithm to conduct value iteration over the selected subset. The algorithm is attractive in that it works with belief subset but also retains the quality of the generated values. Given a POMDP, we show how to a priori determine whether the selected subset is a proper subset of belief space. If this is the case, the algorithm carries the advantages of representation in space and efficiency in time.