Markov Decision Processes under External Temporal Processes (2305.16056v3)

Abstract: Most reinforcement learning algorithms treat the context under which they operate as a stationary, isolated, and undisturbed environment. However, in real world applications, environments constantly change due to a variety of external events. To address this problem, we study Markov Decision Processes (MDP) under the influence of an external temporal process. First, we formalize this notion and derive 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. Our analysis addresses the non-stationarity present in the MDP as a result of non-Markovian events, necessitating the formulation of policies that are contingent upon both the current state and a history of prior events. Additionally, we derive insights regarding the sample complexity of the algorithm and incorporate factors that define the exogenous temporal process into the established bounds. Finally, we perform experiments to demonstrate our findings within a traditional control environment.