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We propose a novel constrained reinforcement learning method for findingoptimal policies in Markov Decision Processes while satisfying temporal logicconstraints with a desired probability throughout the learning process. Anautomata-theoretic approach is proposed to ensure the probabilisticsatisfaction of the constraint in each episode, which is different frompenalizing violations to achieve constraint satisfaction after a sufficientlylarge number of episodes. The proposed approach is based on computing a lowerbound on the probability of constraint satisfaction and adjusting theexploration behavior as needed. We present theoretical results on theprobabilistic constraint satisfaction achieved by the proposed approach. Wealso numerically demonstrate the proposed idea in a drone scenario, where theconstraint is to perform periodically arriving pick-up and delivery tasks andthe objective is to fly over high-reward zones to simultaneously perform aerialmonitoring.

Probabilistically Guaranteed Satisfaction of Temporal Logic Constraints During Reinforcement Learning