Value-Directed Belief State Approximation for POMDPs
This work addresses belief-state monitoring for POMDP policies, offering a novel approach that could improve decision-making in domains like robotics or AI planning, though it appears incremental as it builds on existing approximation schemes.
The paper tackles the problem of approximating belief states in partially observable Markov decision processes (POMDPs) by proposing a value-directed framework that focuses on minimizing expected utility error rather than belief state error, and it introduces heuristic methods and algorithms for error bounds.
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 belief-state approximation (e.g., based on minimixing a measures such as KL-diveregence 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 fucntion. 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.