Accelerated decomposition techniques for large discounted Markov decision processes

Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorithm, which is a variant of Tarjan's algorithm that simultaneously finds the SCCs and their belonging levels. Second, a new definition of the restricted MDPs is presented to ameliorate some hierarchical solutions in discounted MDPs using value iteration (VI) algorithm based on a list of state-action successors. Finally, a robotic motion-planning example and the experiment results are presented to illustrate the benefit of the proposed decomposition algorithms.