In this paper, we investigate the combination of synthesis, model-based learning, and online sampling techniques to obtain safe and near-optimal schedulers for a preemptible task scheduling problem. Our algorithms can handle Markov decision processes (MDPs) that have 1020 states and beyond which cannot be handled with state-of-the art probabilistic model-checkers. We provide probably approximately correct (PAC) guarantees for learning the model. Additionally, we extend Monte-Carlo tree search with advice, computed using safety games or obtained using the earliest-deadline-first scheduler, to safely explore the learned model online. Finally, we implemented and compared our algorithms empirically against shielded deep Q-learning on large task systems.
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