  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.
