Rao-Blackwellized POMDP Planning

TL;DR

This paper introduces Rao-Blackwellized POMDP solvers that improve belief update efficiency and planning accuracy in high-dimensional, uncertain environments compared to traditional particle filters.

Contribution

It proposes a novel Rao-Blackwellized approach for POMDP belief updates and planning, demonstrating improved performance over standard particle filters in simulated localization tasks.

Findings

RBPFs maintain accurate beliefs with fewer particles.

RBPF combined with quadrature enhances planning quality.

RBPF outperforms SIRPF in computational efficiency and accuracy.

Abstract

Partially Observable Markov Decision Processes (POMDPs) provide a structured framework for decision-making under uncertainty, but their application requires efficient belief updates. Sequential Importance Resampling Particle Filters (SIRPF), also known as Bootstrap Particle Filters, are commonly used as belief updaters in large approximate POMDP solvers, but they face challenges such as particle deprivation and high computational costs as the system's state dimension grows. To address these issues, this study introduces Rao-Blackwellized POMDP (RB-POMDP) approximate solvers and outlines generic methods to apply Rao-Blackwellization in both belief updates and online planning. We compare the performance of SIRPF and Rao-Blackwellized Particle Filters (RBPF) in a simulated localization problem where an agent navigates toward a target in a GPS-denied environment using POMCPOW and RB-POMCPOW planners. Our results not only confirm that RBPFs maintain accurate belief approximations over time with fewer particles, but, more surprisingly, RBPFs combined with quadrature-based integration improve planning quality significantly compared to SIRPF-based planning under the same computational limits.