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A PAC Learning Algorithm for LTL and Omega-regular Objectives in MDPs
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Linear temporal logic (LTL) and omega-regular objectives -- a superset of LTL -- have seen recent use as a way to express non-Markovian objectives in reinforcement learning. We introduce a model-based probably approximately correct (PAC) learning algorithm for omega-regular objectives in Markov decision processes (MDPs). As part of the development of our algorithm, we introduce the epsilon-recurrence time: a measure of the speed at which a policy converges to the satisfaction of the omega-regular objective in the limit. We prove that our algorithm only requires a polynomial number of samples in the relevant parameters, and perform experiments which confirm our theory.
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Regret-Free Reinforcement Learning for LTL Specifications
A regret-free (sublinear-regret) episodic algorithm for LTL objectives, built on optimistic interval-MDP value iteration for reach-avoid and a graph-learning preprocess requiring a known minimum transition probability.
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