  In most common settings of Markov Decision Process (MDP), an agent evaluate a
policy based on expectation of (discounted) sum of rewards. However in many
applications this criterion might not be suitable from two perspective: first,
in risk aversion situation expectation of accumulated rewards is not robust
enough, this is the case when distribution of accumulated reward is heavily
skewed; another issue is that many applications naturally take several
objective into consideration when evaluating a policy, for instance in
autonomous driving an agent needs to balance speed and safety when choosing
appropriate decision. In this paper, we consider evaluating a policy based on a
sequence of quantiles it induces on a set of target states, our idea is to
reformulate the original problem into a multi-objective MDP problem with
lexicographic preference naturally defined. For computation of finding an
optimal policy, we proposed an algorithm \textbf{FLMDP} that could solve
general multi-objective MDP with lexicographic reward preference.
