Solving Hidden-Semi-Markov-Mode Markov Decision Problems

Abstract

Hidden-Mode Markov Decision Processes (HM-MDPs) were proposed to represent sequential decision-making problems in non-stationary environments that evolve according to a Markov chain. We introduce in this paper Hidden-Semi-Markov-Mode Markov Decision Process es (HS3MDPs), a generalization of HM-MDPs to the more realistic case of non-stationary environments evolving according to a semi-Markov chain. Like HM-MDPs, HS3MDPs form a subclass of Partially Observable Markov Decision Processes. Therefore, large instances of HS3MDPs (and HM-MDPs) can be solved using an online algorithm, the Partially Observable Monte Carlo Planning (POMCP) algorithm, based on Monte Carlo Tree Search exploiting particle filters for belief state approximation. We propose a first adaptation of POMCP to solve HS3MDPs more efficiently by exploiting their structure. Our empirical results show that the first adapted POMCP reaches higher cumulative rewards than the original algorithm. However, in larger instances, POMCP may run out of particles. To solve this issue, we propose a second adaptation of POMCP, replacing particle filters by exact representations of beliefs. Our empirical results indicate that this new version reaches high cumulative rewards faster than the former adapted POMCP and still remains efficient even for large problems.