Most reinforcement learning algorithms treat the context under which they operate as a stationary, isolated and undisturbed environment. However, in the real world, the environment is constantly changing due to a variety of external influences. To address this problem, we study Markov Decision Processes (MDP) under the influence of an external temporal process. We formalize this notion and discuss conditions under which the problem becomes tractable with suitable solutions. We propose a policy iteration algorithm to solve this problem and theoretically analyze its performance.

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