Online Learning of Safety function for Markov Decision Processes

In this paper, we aim to study safety specifications for a Markov decision process with stochastic stopping time in an almost model-free setting. Our approach involves characterizing a proxy set of the states that are near in a probabilistic sense to the set of unsafe states - forbidden set. We also provide results that relate safety function with reinforcement learning. Consequently, we develop an online algorithm based on the temporal difference method to compute the safety function. Finally, we provide simulation results that demonstrate our work in a simple example.