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Reinforcement Learning Dynamics in the Infinite Memory Limit

Reinforcement learning algorithms have been shown to converge to the classic replicator dynamics of evolutionary game theory, which describe the evolutionary process in the limit of an infinite population. However, it is not clear how to interpret these dynamics from the perspective of a learning agent. In this paper we propose a data-inefficient batch-learning algorithm for temporal difference Q learning and show that it converges to a recently proposed deterministic limit of temporal difference reinforcement learning. In a second step, we state a data-efficient learning algorithm, that uses a form of experience replay, and show that it retains core features of the batch learning algorithm. Thus, we propose an agent-interpretation for the learning dynamics: What is the infinite population limit of evolutionary dynamics is the infinite memory limit of learning dynamics.