  We consider the problem of constrained Markov decision process (CMDP) in
continuous state-actions spaces where the goal is to maximize the expected
cumulative reward subject to some constraints. We propose a novel Conservative
Natural Policy Gradient Primal-Dual Algorithm (C-NPG-PD) to achieve zero
constraint violation while achieving state of the art convergence results for
the objective value function. For general policy parametrization, we prove
convergence of value function to global optimal upto an approximation error due
to restricted policy class. We even improve the sample complexity of existing
constrained NPG-PD algorithm \cite{Ding2020} from $\mathcal{O}(1/\epsilon^6)$
to $\mathcal{O}(1/\epsilon^4)$. To the best of our knowledge, this is the first
work to establish zero constraint violation with Natural policy gradient style
algorithms for infinite horizon discounted CMDPs. We demonstrate the merits of
proposed algorithm via experimental evaluations.
