Mori-zwanzig approach for belief abstraction with application to belief space planning

We propose a learning-based method to extract symbolic representations of the belief state and its dynamics in order to solve planning problems in a continuous-state partially observable Markov decision processes (POMDP) problem. While existing approaches typically parameterize the continuous-state POMDP into a finite-dimensional Markovian model, they are unable to preserve fidelity of the abstracted model. To improve accuracy of the abstracted representation, we introduce a memory-dependent abstraction approach to mitigate the modeling error. The first major contribution of this paper is we propose a Neural Network based method to learn the non-Markovian transition model based on the Mori-Zwanzig (M-Z) formalism. Different from existing work in applying M-Z formalism to autonomous time-invariant systems, our approach is the first work generalizing the M-Z formalism to robotics, by addressing the non-Markovian modeling of the belief dynamics that is dependent on historical observations and actions. The second major contribution is we theoretically show that modeling the non-Markovian memory effect in the abstracted belief dynamics improves the modeling accuracy, which is the key benefit of the proposed algorithm. Simulation experiment of a belief space planning problem is provided to validate the performance of the proposed belief abstraction algorithms.