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：许多现实机器人技术与规划问题需要处理具有高维连续观测（如相机图像）的部分可观测马尔可夫决策过程（POMDP）。近期研究表明机器学习概率模型可作为观测模型，但其在线部署的计算成本过高。本文探讨在保留解决方案质量形式化保证的前提下，采用简化观测模型进行规划的潜在影响。我们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。通过推广近期粒子信念MDP浓度界的研究成果，我们证明该界能够从简化模型的经验规划值出发，约束相对于原始模型的理论POMDP值。计算过程可拆分为离线和在线两个部分，从而在规划过程中完全无需访问昂贵模型即可获得形式化保证——这同样属于创新性成果。最后通过仿真实验展示如何将该界集成到现有连续在线POMDP求解器的常规流程中。