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Maintenance is of great importance for the safety and integrity of infrastructures. The expected optimal maintenance policy in this study should be able to minimize system maintenance cost while satisfying the system reliability requirements. Stochastic maintenance scheduling with an infinite horizon has not been investigated thoroughly in the literature. In this work, we formulate the maintenance optimization under uncertainties as a Markov Decision Process (MDP) problem and solve it using a modified Reinforcement Learning method. A Linear Programming-enhanced RollouT (LPRT) is proposed, which considers both constrained deterministic and stochastic maintenance scheduling with an infinite horizon. The novelty of the proposed approach is that it is suitable for online maintenance scheduling, which can include random unexpected maintenance performance and system degradation. The proposed method …