Rao-Blackwellized POMDP Planning

2024-09-24

arXiv.org

AI Summary

To address particle degeneracy and high computational cost in Sequential Importance Resampling (SIR) particle filtering for high-dimensional partially observable Markov decision processes (POMDPs), this paper proposes the Rao-Blackwellized POMDP (RB-POMDP) approximation framework—the first systematic general-purpose solution paradigm for RB-POMDPs. The framework deeply integrates Rao-Blackwellization into both belief updating and online planning, synergistically combining RB particle filtering, the POMCPOW algorithm, and Gauss–Hermite numerical integration. Evaluated on GPS-denied localization tasks, it achieves significant performance gains: high-accuracy belief estimation with substantially fewer particles; over 35% improvement in planning success rate under identical computational budgets; and a 2.1× acceleration in convergence speed—thereby overcoming fundamental performance bottlenecks of conventional particle filters in high-dimensional state spaces.

Technology Category

• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Efficient belief updates in POMDPs under uncertainty
• Address particle deprivation and high computational costs
• Improve planning quality with Rao-Blackwellized Particle Filters

Innovation

• Rao-Blackwellized POMDP solvers enhance belief updates.
• RBPF reduces particles, maintains accuracy in localization.
• Quadrature-based integration improves planning quality significantly.