Unbounded Human Learning: Optimal Scheduling for Spaced Repetition. (arXiv:1602.07032v1 [cs.AI])

In the study of human learning, there is broad evidence that our ability to retain a piece of information improves with repeated exposure, and that it decays with delay since the last exposure. This plays a crucial role in the design of educational software, leading to a trade-off between teaching new material and reviewing what has already been taught. A common way to balance this trade-off is via spaced repetition -- using periodic review of content to improve long-term retention. Though widely used in practice, there is little formal understanding of the design of these systems. This paper addresses this gap. First, we mine log data from a spaced repetition system to establish the functional dependence of retention on reinforcement and delay. Second, based on this memory model, we develop a mathematical framework for spaced repetition systems using a queueing-network approach. This model formalizes the popular Leitner Heuristic for spaced repetition, providing the first rigorous and computationally tractable means of optimizing the review schedule. Finally, we empirically confirm the validity of our formal model via a Mechanical Turk experiment. In particular, we verify a key qualitative insight and prediction of our model -- the existence of a sharp phase transition in learning outcomes upon increasing the rate of new item introductions.

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