Learning with Safety Constraints: Sample Complexity of Reinforcement Learning for Constrained MDPs

Many physical systems have underlying safety considerations that require that the policy employed ensures the satisfaction of a set of constraints. The analytical formulation usually takes the form of a Constrained Markov Decision Process (CMDP), where the constraints are some function of the occupancy measure generated by the policy. We focus on the case where the CMDP is unknown, and RL algorithms obtain samples to discover the model and compute an optimal constrained policy. Our goal is to characterize the relationship between safety constraints and the number of samples needed to ensure a desired level of accuracy---both objective maximization and constraint satisfaction---in a PAC sense. We explore generative model based class of RL algorithms wherein samples are taken initially to estimate a model. Our main finding is that compared to the best known bounds of the unconstrained regime, the sample complexity of constrained RL algorithms are increased by a factor that is logarithmic in the number of constraints, which suggests that the approach may be easily utilized in real systems.