  Unlike the standard Reinforcement Learning (RL) model, many real-world tasks
are non-Markovian, whose rewards are predicated on state history rather than
solely on the current state. Solving a non-Markovian task, frequently applied
in practical applications such as autonomous driving, financial trading, and
medical diagnosis, can be quite challenging. We propose a novel RL approach to
achieve non-Markovian rewards expressed in temporal logic LTL$_f$ (Linear
Temporal Logic over Finite Traces). To this end, an encoding of linear
complexity from LTL$_f$ into MDPs (Markov Decision Processes) is introduced to
take advantage of advanced RL algorithms. Then, a prioritized experience replay
technique based on the automata structure (semantics equivalent to LTL$_f$
specification) is utilized to improve the training process. We empirically
evaluate several benchmark problems augmented with non-Markovian tasks to
demonstrate the feasibility and effectiveness of our approach.
