Enhancing human learning via spaced repetition optimization

Behzad Tabibian,Utkarsh Upadhyay,Abir De,Ali Zarezade,Bernhard Schölkopf,Manuel Gomez-Rodriguez

doi:10.1073/pnas.1815156116

Abstract

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.

Highlights

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
Our ability to remember a piece of information depends critically on the number of times we have reviewed it, the temporal distribution of the reviews, and the time elapsed since the last review, as first shown by a seminal study by Ebbinghaus [1]. The effect of these two factors has been extensively investigated in the experimental psychology literature [2, 3], in second language acquisition research [4,5,6,7]. These empirical studies have motivated the use of flashcards, small pieces of information a learner repeatedly reviews following a schedule determined by a spaced repetition algorithm [8], whose goal is to ensure that learners spend more time working on forgotten information
The researchers have proposed heuristic algorithms that decide which item to review by greedily selecting the item which is closest to its maximum learning rate

Summary

Introduction

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. Most of the above spaced repetition algorithms are simple rule-based heuristics with a few hardcoded parameters [8], which are unable to fulfill this promise— adaptive, data-driven algorithms with provable guarantees have been largely missing until very recently [14, 15] Among these recent notable exceptions, the work most closely related to ours is by Reddy et al [15], who proposed a queueing network model for a particular spaced repetition method—the Leitner system [9] for reviewing flashcards—and developed a heuristic approximation algorithm for scheduling reviews. The researchers have proposed heuristic algorithms that decide which item to review by greedily selecting the item which is closest to its maximum learning rate

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Results