Value-Directed Belief State Approximation for POMDPs

TL;DR

This paper introduces a value-directed approach for approximating belief states in POMDPs, focusing on utility error rather than belief accuracy, and proposes heuristic methods and algorithms for error bounding.

Contribution

It presents a novel framework for belief-state approximation in POMDPs that prioritizes decision quality and utility, along with heuristic schemes and error bounds.

Findings

Heuristic projection schemes improve belief state estimation.

Algorithms effectively bound decision quality errors.

Value-directed approximation outperforms traditional methods.

Abstract

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.