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We consider the problem of finding optimal policies for a Markov DecisionProcess with almost sure constraints on state transitions and action triplets.We define value and action-value functions that satisfy a barrier-baseddecomposition which allows for the identification of feasible policiesindependently of the reward process. We prove that, given a policy {\pi},certifying whether certain state-action pairs lead to feasible trajectoriesunder {\pi} is equivalent to solving an auxiliary problem aimed at finding theprobability of performing an unfeasible transition. Using thisinterpretation,we develop a Barrier-learning algorithm, based on Q-Learning,that identifies such unsafe state-action pairs. Our analysis motivates the needto enhance the Reinforcement Learning (RL) framework with an additional signal,besides rewards, called here damage function that provides feasibilityinformation and enables the solution of RL problems with model-freeconstraints. Moreover, our Barrier-learning algorithm wraps around existing RLalgorithms, such as Q-Learning and SARSA, giving them the ability to solvealmost-surely constrained problems.

Assured RL: Reinforcement Learning with Almost Sure Constraints