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Linear Temporal Logic (LTL) is widely used to specify high-level objectivesfor system policies, and it is highly desirable for autonomous systems to learnthe optimal policy with respect to such specifications. However, learning theoptimal policy from LTL specifications is not trivial. We present a model-freeReinforcement Learning (RL) approach that efficiently learns an optimal policyfor an unknown stochastic system, modelled using Markov Decision Processes(MDPs). We propose a novel and more general product MDP, reward structure anddiscounting mechanism that, when applied in conjunction with off-the-shelfmodel-free RL algorithms, efficiently learn the optimal policy that maximizesthe probability of satisfying a given LTL specification with optimalityguarantees. We also provide improved theoretical results on choosing the keyparameters in RL to ensure optimality. To directly evaluate the learned policy,we adopt probabilistic model checker PRISM to compute the probability of thepolicy satisfying such specifications. Several experiments on various tabularMDP environments across different LTL tasks demonstrate the improved sampleefficiency and optimal policy convergence.

Sample Efficient Model-free Reinforcement Learning from LTL Specifications with Optimality Guarantees