Applying Metric-Trees to Belief-Point POMDPs

Recent developments in grid-based and point-based approximation algorithms forPOMDPs have greatly improved the tractability of POMDP planning. These approaches operate on sets of belief points by individually learninga value function for each point. In reality, belief points exist in a highly-structured metric simplex, but current POMDP algorithms donot exploit this property. This paper presents a new metric-tree algorithm which can be used in the context of POMDP planning to sort belief points spatially, and then perform fast value function updates over groups of points. We present results showing that this approach can reduce computationin point-based POMDP algorithms for a wide range of problems.