  Reinforcement learning is widely used in applications where one needs to
perform sequential decisions while interacting with the environment. The
problem becomes more challenging when the decision requirement includes
satisfying some safety constraints. The problem is mathematically formulated as
constrained Markov decision process (CMDP). In the literature, various
algorithms are available to solve CMDP problems in a model-free manner to
achieve $\epsilon$-optimal cumulative reward with $\epsilon$ feasible policies.
An $\epsilon$-feasible policy implies that it suffers from constraint
violation. An important question here is whether we can achieve
$\epsilon$-optimal cumulative reward with zero constraint violations or not. To
achieve that, we advocate the use of randomized primal-dual approach to solve
the CMDP problems and propose a conservative stochastic primal-dual algorithm
(CSPDA) which is shown to exhibit
$\tilde{\mathcal{O}}\left(1/\epsilon^2\right)$ sample complexity to achieve
$\epsilon$-optimal cumulative reward with zero constraint violations. In the
prior works, the best available sample complexity for the $\epsilon$-optimal
policy with zero constraint violation is
$\tilde{\mathcal{O}}\left(1/\epsilon^5\right)$. Hence, the proposed algorithm
provides a significant improvement as compared to the state of the art.
