  A new mechanism for efficiently solving the Markov decision processes (MDPs)
is proposed in this paper. We introduce the notion of reachability landscape
where we use the Mean First Passage Time (MFPT) as a means to characterize the
reachability of every state in the state space. We show that such reachability
characterization very well assesses the importance of states and thus provides
a natural basis for effectively prioritizing states and approximating policies.
Built on such a novel observation, we design two new algorithms -- Mean First
Passage Time based Value Iteration (MFPT-VI) and Mean First Passage Time based
Policy Iteration (MFPT-PI) -- that have been modified from the state-of-the-art
solution methods. To validate our design, we have performed numerical
evaluations in robotic decision-making scenarios, by comparing the proposed new
methods with corresponding classic baseline mechanisms. The evaluation results
showed that MFPT-VI and MFPT-PI have outperformed the state-of-the-art
solutions in terms of both practical runtime and number of iterations. Aside
from the advantage of fast convergence, this new solution method is intuitively
easy to understand and practically simple to implement.
