Anytime Incremental $ ho$POMDP Planning in Continuous Spaces

2025-02-04

AI Summary

Existing online ρPOMDP solvers employ fixed belief representations in continuous state spaces, resulting in poor adaptivity, limited refinement capability, and high computational overhead for belief-dependent reward evaluation. This paper introduces ρPOMCPOW—the first anytime-convergent, incremental online ρPOMDP solver—unifying Monte Carlo tree search, particle filtering, incremental entropy estimation, and adaptive belief sampling to enable dynamic belief refinement and efficient reward assessment. We provide theoretical guarantees of asymptotic convergence and monotonic policy improvement. Empirical evaluations on information-gathering tasks demonstrate significant performance gains over baseline methods: ρPOMCPOW achieves order-of-magnitude speedup in belief-dependent reward computation while maintaining real-time execution and high-quality decision-making.

Technology Category

• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Reasoning under Uncertainty: Sequential Decision Making
• Machine Learning: Online Learning & Bandits

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

Abstract

Partially Observable Markov Decision Processes (POMDPs) provide a robust framework for decision-making under uncertainty in applications such as autonomous driving and robotic exploration. Their extension, $ ho$POMDPs, introduces belief-dependent rewards, enabling explicit reasoning about uncertainty. Existing online $ ho$POMDP solvers for continuous spaces rely on fixed belief representations, limiting adaptability and refinement - critical for tasks such as information-gathering. We present $ ho$POMCPOW, an anytime solver that dynamically refines belief representations, with formal guarantees of improvement over time. To mitigate the high computational cost of updating belief-dependent rewards, we propose a novel incremental computation approach. We demonstrate its effectiveness for common entropy estimators, reducing computational cost by orders of magnitude. Experimental results show that $ ho$POMCPOW outperforms state-of-the-art solvers in both efficiency and solution quality.

Problem

• Dynamic refinement of belief representations
• Incremental computation for belief-dependent rewards
• Improvement in efficiency and solution quality

Innovation

• Dynamic belief representation refinement
• Incremental reward computation approach
• Efficient entropy estimation reduction