  In this paper, we present an online reinforcement learning algorithm for
constrained Markov decision processes with a safety constraint. Despite the
necessary attention of the scientific community, considering stochastic
stopping time, the problem of learning optimal policy without violating safety
constraints during the learning phase is yet to be addressed. To this end, we
propose an algorithm based on linear programming that does not require a
process model. We show that the learned policy is safe with high confidence. We
also propose a method to compute a safe baseline policy, which is central in
developing algorithms that do not violate the safety constraints. Finally, we
provide simulation results to show the efficacy of the proposed algorithm.
Further, we demonstrate that efficient exploration can be achieved by defining
a subset of the state-space called proxy set.
