连续空间中的随时增量式ρPOMDP规划
Anytime Incremental $ρ$POMDP Planning in Continuous Spaces
AI总结：
本文提出随时求解器ρPOMCPOW，通过动态细化信念表示和增量计算依赖信念奖励，在连续空间ρPOMDP规划中显著提升效率与求解质量。
摘要：
部分可观测马尔可夫决策过程（POMDPs）为自动驾驶和机器人探索等应用中的不确定性决策提供了稳健框架。其扩展形式ρPOMDPs引入了依赖信念的奖励，能够对不确定性进行显式推理。现有的连续空间在线ρPOMDP求解器依赖固定的信念表示，限制了适应性和细化能力——这对于信息收集等任务至关重要。我们提出了ρPOMCPOW，一种随时求解器，可动态细化信念表示，并具有随时间改进的形式化保证。为缓解更新依赖信念奖励的高计算成本，我们提出了一种新颖的增量计算方法。我们证明了该方法对常见熵估计器的有效性，将计算成本降低了数个数量级。实验结果表明，ρPOMCPOW在效率和求解质量上均优于最先进的求解器。
英文摘要：
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, $ρ$POMDPs, introduces belief-dependent rewards, enabling explicit reasoning about uncertainty. Existing online $ρ$POMDP solvers for continuous spaces rely on fixed belief representations, limiting adaptability and refinement - critical for tasks such as information-gathering. We present $ρ$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 $ρ$POMCPOW outperforms state-of-the-art solvers in both efficiency and solution quality.
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