Open-loop POMDP Simplification and Safe Skipping of Replanning with Formal Performance Guarantees

2026-04-01

AI Summary

This work addresses the challenge of intractable exact solution for partially observable Markov decision processes (POMDPs) due to their high computational complexity by proposing an adaptive open-loop simplification framework. The approach constructs a belief tree based on topological structure and alternates between open-loop and closed-loop planning. It introduces, for the first time, a safety-aware replanning-skipping mechanism for multi-step open-loop action sequences with formal performance guarantees. By deriving efficiently computable performance bounds, the method ensures that the simplified planning process still identifies the optimal immediate action of the original problem. Experimental results demonstrate that the proposed framework significantly reduces planning overhead while preserving provable performance guarantees, thereby substantially improving the scalability and efficiency of online POMDP solvers.

Abstract

Partially Observable Markov Decision Processes (POMDPs) provide a principled mathematical framework for decision-making under uncertainty. However, the exact solution to POMDPs is computationally intractable. In this paper, we address the computational intractability by introducing a novel framework for adaptive open-loop simplification with formal performance guarantees. Our method adaptively interleaves open-loop and closed-loop planning via a topology-based belief tree, enabling a significant reduction in planning complexity. The key contribution lies in the derivation of efficiently computable bounds which provide formal guarantees and can be used to ensure that our simplification can identify the immediate optimal action of the original POMDP problem. Our framework therefore provides computationally tractable performance guarantees for macro-actions within POMDPs. Furthermore, we propose a novel framework for safely skipping replanning during execution, supported by theoretical guarantees on multi-step open-loop action sequences. To the best of our knowledge, this framework is the first to address skipping replanning with formal performance guarantees. Practical online solvers for our proposed simplification are developed, including a sampling-based solver and an anytime solver. Empirical results demonstrate substantial computational speedups while maintaining provable performance guarantees, advancing the tractability and efficiency of POMDP planning.

Problem

• POMDP
• computational intractability
• decision-making under uncertainty
• planning complexity
• replanning

Innovation

• POMDP simplification
• open-loop planning
• formal performance guarantees
• replanning skipping
• belief tree