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Many physical systems have underlying safety considerations that require thatthe policy employed ensures the satisfaction of a set of constraints. Theanalytical formulation usually takes the form of a Constrained Markov DecisionProcess (CMDP). We focus on the case where the CMDP is unknown, and RLalgorithms obtain samples to discover the model and compute an optimalconstrained policy. Our goal is to characterize the relationship between safetyconstraints and the number of samples needed to ensure a desired level ofaccuracy -- both objective maximization and constraint satisfaction -- in a PACsense. We explore two classes of RL algorithms, namely, (i) a generative modelbased approach, wherein samples are taken initially to estimate a model, and(ii) an online approach, wherein the model is updated as samples are obtained.Our main finding is that compared to the best known bounds of the unconstrainedregime, the sample complexity of constrained RL algorithms are increased by afactor that is logarithmic in the number of constraints, which suggests thatthe approach may be easily utilized in real systems.

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