Value-Directed Belief State Approximation for POMDPs

We consider the problem belief-state monitoring for the purposes of implementing a policy for a partially-observable Markov decision process (POMDP), specifically how one might approximate the belief state. Other schemes for beliefstate approximation (e.g., based on minimizing a measure such as KL-divergence between the true and estimated state) are not necessarily appropriate for POMDPs. Instead we propose a framework for analyzing value-directed approximation schemes, where approximation quality is determined by the expected error in utility rather than by the error in the belief state itself. We propose heuristic methods for finding good projection schemes for belief state estimation--exhibiting anytime characteristics--given a POMDP value function. We also describe several algorithms for constructing bounds on the error in decision quality (expected utility) associated with acting in accordance with a given belief state approximation.