arXiv:2604.01352cs.RO2026-04中稿 · WAFR 2026被引 1

提出可保证安全的开环简化方法,显著降低不确定环境下的决策计算负担。

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

  • 基于信念树动态切换开环与闭环规划,减少复杂度
  • 给出可计算的性能界,确保简化后动作仍最优
  • 支持执行中安全跳过重规划,适合实时决策系统

部分可观测马尔可夫决策过程(POMDP)为不确定性下的决策提供了严谨的数学框架,但其精确解在计算上不可行。本文提出一种自适应开环简化框架,结合拓扑结构的信念树,实现开环与闭环规划的动态交替,显著降低规划复杂度。核心贡献在于推导出高效可计算的性能边界,可形式化保证简化后的动作与原问题的即时最优动作一致。该框架为POMDP中的宏观动作提供可计算的性能保证。此外,我们提出一种安全跳过重规划的新方法,基于多步开环动作序列的理论保证。据我们所知,这是首个在跳过重规划时提供形式化性能保证的框架。开发了实用的在线求解器,包括采样求解器和任意时求解器。实验表明,该方法在保持可证明性能保障的同时实现显著计算加速,提升了POMDP规划的可处理性与效率。

原文摘要 · Abstract (English)

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.

POMDP决策规划形式保证实时控制

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