Spaced repetition is a technique for efficient memorization which uses repeated, spaced review of content to improve long-term retention. Can we find the optimal reviewing schedule to maximize the benefits of spaced repetition? In this paper, we introduce a novel, flexible representation of spaced repetition using the framework of marked temporal point processes and then address the above question as an optimal control problem for stochastic differential equations with jumps. For two well-known human memory models, we show that the optimal reviewing schedule is given by the recall probability of the content to be learned. As a result, we can then develop a simple, scalable online algorithm, Memorize, to sample the optimal reviewing times. Experiments on both synthetic and real data gathered from Duolingo, a popular language-learning online platform, show that our algorithm may be able to help learners memorize more effectively than alternatives.

Optimizing Human Learning