Abstract
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.