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We study entropy-regularized constrained Markov decision processes (CMDPs)under the soft-max parameterization, in which an agent aims to maximize theentropy-regularized value function while satisfying constraints on the expectedtotal utility. By leveraging the entropy regularization, our theoreticalanalysis shows that its Lagrangian dual function is smooth and the Lagrangianduality gap can be decomposed into the primal optimality gap and the constraintviolation. Furthermore, we propose an accelerated dual-descent method forentropy-regularized CMDPs. We prove that our method achieves the globalconvergence rate $\widetilde{\mathcal{O}}(1/T)$ for both the optimality gap andthe constraint violation for entropy-regularized CMDPs. A discussion about alinear convergence rate for CMDPs with a single constraint is also provided.

A Dual Approach to Constrained Markov Decision Processes with Entropy Regularization