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In most common settings of Markov Decision Process (MDP), an agent evaluate apolicy based on expectation of (discounted) sum of rewards. However in manyapplications this criterion might not be suitable from two perspective: first,in risk aversion situation expectation of accumulated rewards is not robustenough, this is the case when distribution of accumulated reward is heavilyskewed; another issue is that many applications naturally take severalobjective into consideration when evaluating a policy, for instance inautonomous driving an agent needs to balance speed and safety when choosingappropriate decision. In this paper, we consider evaluating a policy based on asequence of quantiles it induces on a set of target states, our idea is toreformulate the original problem into a multi-objective MDP problem withlexicographic preference naturally defined. For computation of finding anoptimal policy, we proposed an algorithm \textbf{FLMDP} that could solvegeneral multi-objective MDP with lexicographic reward preference.

Solving Multi-Objective MDP with Lexicographic Preference: An application to stochastic planning with multiple quantile objective