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A new mechanism for efficiently solving the Markov decision processes (MDPs)is proposed in this paper. We introduce the notion of reachability landscapewhere we use the Mean First Passage Time (MFPT) as a means to characterize thereachability of every state in the state space. We show that such reachabilitycharacterization very well assesses the importance of states and thus providesa natural basis for effectively prioritizing states and approximating policies.Built on such a novel observation, we design two new algorithms -- Mean FirstPassage Time based Value Iteration (MFPT-VI) and Mean First Passage Time basedPolicy Iteration (MFPT-PI) -- that have been modified from the state-of-the-artsolution methods. To validate our design, we have performed numericalevaluations in robotic decision-making scenarios, by comparing the proposed newmethods with corresponding classic baseline mechanisms. The evaluation resultsshowed that MFPT-VI and MFPT-PI have outperformed the state-of-the-artsolutions in terms of both practical runtime and number of iterations. Asidefrom the advantage of fast convergence, this new solution method is intuitivelyeasy to understand and practically simple to implement.

Solving Markov Decision Processes with Reachability Characterization from Mean First Passage Times