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arXiv · 2310.12248

A PAC Learning Algorithm for LTL and Omega-regular Objectives in MDPs

Mateo Perez·Fabio Somenzi·Ashutosh Trivedi
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Abstract

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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Mateo Perez, Fabio Somenzi, Ashutosh Trivedi. 2023-10-18. A PAC Learning Algorithm for LTL and Omega-regular Objectives in MDPs. https://arxiv.org/abs/2310.12248

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