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：解决具有高维连续观测（如相机图像）的部分可观测马尔可夫决策过程（POMDP）是许多实际机器人学及规划问题所需。近期研究表明机器学习概率模型可作为观测模型，但其在在线部署中计算成本过高。我们探讨了在规划中使用简化观测模型的同时保持解质量形式化保证的可行性。本文主要贡献在于提出一种基于简化模型统计总变差距离的新型概率界。通过泛化近期粒子置信MDP浓度界的研究成果，我们证明了该界能够将基于简化模型的经验规划值约束为相对原始模型的理论POMDP值。所提计算可分解为离线与在线两部分，从而在规划全程无需访问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，我们在仿真中演示了如何将该界集成至现有连续在线POMDP求解器的常规流程中。