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We study the relation between different Markov Decision Process (MDP)frameworks in the machine learning and econometrics literatures, including thestandard MDP, the entropy and general regularized MDP, and stochastic MDP,where the latter is based on the assumption that the reward function isstochastic and follows a given distribution. We show that theentropy-regularized MDP is equivalent to a stochastic MDP model, and isstrictly subsumed by the general regularized MDP. Moreover, we propose adistributional stochastic MDP framework by assuming that the distribution ofthe reward function is ambiguous. We further show that the distributionalstochastic MDP is equivalent to the regularized MDP, in the sense that theyalways yield the same optimal policies. We also provide a connection betweenstochastic/regularized MDP and constrained MDP. Our work gives a unified viewon several important MDP frameworks, which would lead new ways to interpret the(entropy/general) regularized MDP frameworks through the lens of stochasticrewards and vice-versa. Given the recent popularity of regularized MDP in(deep) reinforcement learning, our work brings new understandings of how suchalgorithmic schemes work and suggest ideas to develop new ones.

A Relation Analysis of Markov Decision Process Frameworks