Faster algorithm and sharper analysis for constrained Markov decision process

The problem of constrained Markov decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated reward subject to constraints on its utilities/costs. We propose a new primal-dual approach with a novel integration of entropy regularization and Nesterov's accelerated gradient method. The proposed approach is shown to converge to the global optimum with a complexity of $\widetilde{𝒪}(1/ϵ)$ in terms of the optimality gap and the constraint violation, which improves the complexity of the existing primal-dual approaches by a factor of $𝒪(1/ϵ)$ .