  The problem of constrained Markov decision process is considered. An agent
aims to maximize the expected accumulated discounted reward subject to multiple
constraints on its costs (the number of constraints is relatively small). A new
dual approach is proposed with the integration of two ingredients: entropy
regularized policy optimizer and Vaidya's dual optimizer, both of which are
critical to achieve faster convergence. The finite-time error bound of the
proposed approach is provided. Despite the challenge of the nonconcave
objective subject to nonconcave constraints, the proposed approach is shown to
converge (with linear rate) to the global optimum. The complexity expressed in
terms of the optimality gap and the constraint violation significantly improves
upon the existing primal-dual approaches.
