Enhancing human learning via spaced repetition optimization

Significance Understanding human memory has been a long-standing problem in various scientific disciplines. Early works focused on characterizing human memory using small-scale controlled experiments and these empirical studies later motivated the design of spaced repetition algorithms for efficient memorization. However, current spaced repetition algorithms are rule-based heuristics with hard-coded parameters, which do not leverage the automated fine-grained monitoring and greater degree of control offered by modern online learning platforms. In this work, we develop a computational framework to derive optimal spaced repetition algorithms, specially designed to adapt to the learners’ performance. A large-scale natural experiment using data from a popular language-learning online platform provides empirical evidence that the spaced repetition algorithms derived using our framework are significantly superior to alternatives. Spaced repetition is a technique for efficient memorization which uses repeated review of content following a schedule determined by a spaced repetition algorithm to improve long-term retention. However, current spaced repetition algorithms are simple rule-based heuristics with a few hard-coded parameters. Here, we introduce a flexible representation of spaced repetition using the framework of marked temporal point processes and then address the design of spaced repetition algorithms with provable guarantees as an optimal control problem for stochastic differential equations with jumps. For two well-known human memory models, we show that, if the learner aims to maximize recall probability of the content to be learned subject to a cost on the reviewing frequency, the optimal reviewing schedule is given by the recall probability itself. As a result, we can then develop a simple, scalable online spaced repetition algorithm, MEMORIZE, to determine the optimal reviewing times. We perform a large-scale natural experiment using data from Duolingo, a popular language-learning online platform, and show that learners who follow a reviewing schedule determined by our algorithm memorize more effectively than learners who follow alternative schedules determined by several heuristics.