  This paper considers the distributionally robust chance constrained Markov
decision process with random reward and ambiguous reward distribution. We
consider individual and joint chance constraint cases with Kullback-Leibler
divergence based ambiguity sets centered at elliptical distributions or
elliptical mixture distributions, respectively. We derive tractable
reformulations of the distributionally robust individual chance constrained
Markov decision process problems and design a new hybrid algorithm based on the
sequential convex approximation and line search method for the joint case. We
carry out numerical tests with a machine replacement problem.
