Solving partially observable Markov decision processes (POMDPs) with high dimensional and continuous observations, such as camera images, is required for many real life robotics and planning problems. Recent researches suggested machine learned probabilistic models as observation models, but their use is currently too computationally expensive for online deployment. We deal with the question of what would be the implication of using simplified observation models for planning, while retaining formal guarantees on the quality of the solution. Our main contribution is a novel probabilistic bound based on a statistical total variation distance of the simplified model. We show that it bounds the theoretical POMDP value w.r.t. original model, from the empirical planned value with the simplified model, by generalizing recent results of particle-belief MDP concentration bounds. Our calculations can be separated into offline and online parts, and we arrive at formal guarantees without having to access the costly model at all during planning, which is also a novel result. Finally, we demonstrate in simulation how to integrate the bound into the routine of an existing continuous online POMDP solver.

翻译：解决部分可观测马尔可夫决策过程（POMDP）中涉及高维连续观测（如相机图像）的问题，是许多现实机器人学与规划任务的核心需求。近年研究提出采用机器学习概率模型作为观测模型，但其计算成本过高，难以实现在线部署。本文探讨采用简化观测模型进行规划时，如何在保留解质量形式化保证的前提下降低计算开销。主要贡献在于基于简化模型统计总变分距离的新型概率界：通过推广近期粒子信念MDP浓度界的研究成果，证明该概率界能够从简化模型的经验规划值出发，约束原始模型对应的理论POMDP值。我们的计算可分解为离线与在线两部分，在规划过程中完全无需访问原始高成本模型即可获得形式化保证——这一成果本身亦具创新性。最后通过仿真实验展示了如何将该概率界集成至现有连续在线POMDP求解器的常规流程中。