We present non-Markov decision processes, where rewards and dynamics can depend on the history of events. This is contrast with Markov Decision Processes, where the dependency is limited to the last state and action. We study how to specify non-Markov reward functions and dynamics functions using Linear Temporal Logic on finite traces. The resulting decision processes are called Regular Decision Processes, and we show how to solve them by extending solution techniques for Markov Decision Processes. Then, we turn to Reinforcement Learning. First, we study the Restraining Bolt, a device that enables an agent to learn a specified non-Markov behaviour while relying on the Markov property. Second, we study how an agent can achieve an optimal behaviour in a non-Markov domain, by learning a finite-state automaton that describes rewards and dynamics. Specifically we will cover the following topics: MDP with Non-Markov Rewards, Non-Markov Dynamics, Regular Decision Processes, Restraining Bolts, Linear Time Logic on finite traces as a reward/dynamics specification language, Reinforcement Learning, Deep Reinforcement Learning, Automata Learning. This course is partially based on the work carried out in ERC Advanced Grant WhiteMech and EU ICT-48 TAILOR.
