Let’s flash back to the days when one tried to learn a second language: Whether child or adult, a person’s ability to remember those nouns, verbs, and adjectives depends critically on the number of times the vocabulary is reviewed, the number of hours or days between each review, and the time elapsed since the last repetition. 
Deciphering the way human memory stores information has always been a fascinating topic for scientists. One primary method for successful memorization of information is known to be “spaced repetition” of content. Many empirical studies have been conducted to assess the appropriate spacing, i.e. the best intervals between repetitions, to form an optimal strategy for the process of acquiring, for instance, a foreign language with minimum effort. These studies inspired flashcards, small pieces of information a learner repeatedly reviews, following a certain schedule. 
Needless to say, the physical flashcard has long been replaced by the flashcard 2.0. In the past decade, an entire industry of eLearning platforms spewed out of the ground providing spaced repetition course schedules. However, most of these online learning providers use spaced repetition algorithms that are simple rule-based heuristics with a few hard-coded parameters. To give an example, a learner may be given a word to review in predetermined intervals of 2 days, then 4, then 8 – independent of the individual’s abilities and the varying difficulties of content under study.

Appropriate spacing - It’s all about the intervals between repetitions
A group of scientists from the Max Planck Institute for Intelligent Systems in Tübingen and the Max Planck Institute for Software Systems in Kaiserslautern suggest in a recent work that the classical methods do not leverage the automated fine-grained monitoring and greater degree of control offered by modern online learning platforms. Modern spaced repetition algorithms should be data driven and adapt to the learner’s performance over time, they believe. Staying with the example given earlier, if students are learning a difficult word they may be asked to review that content again in one day instead of two, while for easier content, the student might be asked to review it again in three days. It depends on the probability that this interval maximizes the probability that the learner recalls that content successfully with minimum effort. 
In their work entitled "Enhancing human learning via spaced repetition optimization", published in the prestigious journal PNAS, lead author Behzad Tabibian, together with Utkarsh Upadhyay, Abir De, Ali Zarezade, Bernhard Schölkopf, and Manuel Gomez-Rodriguez, developed a mathematical framework that, given an existing machine learning model of human memory, gives the optimal solution as to how to decide when the best time to review a particular piece of content is. At its core, their algorithm estimates when the best time is to review a word a student wants to permanently remember, all the while avoiding too many attempts, in order to make the learning process as efficient as possible. 
To evaluate their scheduling algorithm, they relied on existing datasets. "We used a dataset released by Duolingo (an online language-learning app) a few years ago. It is a comprehensive dataset that contains fine-grained records of learners’ practices over a period of two weeks", Tabibian explains.

Avoiding unnecessary effort
Empirical evidence presented in this work suggests that spaced repetition algorithms derived using this new framework are superior to alternative heuristic approaches. "Our optimized spaced repetition algorithm, which we dubbed "Memorize", helps learners remember more effectively, while avoiding unnecessary effort, compared to learners who follow schedules determined by alternative heuristics," says Tabibian. As an example he adds, "Let’s say you want to learn the German word Brötchen (a bun or roll). Based on the experience of everybody who has tried learning this word, the algorithm estimates a baseline for how fast learners usually forget this word. When a person studies the word Brötchen for the first time, the algorithm suggests that you should review this word in a day and a half. Based on whether you can recall the meaning of this word at that time, the algorithm suggests when the best time would be to review that word again and so forth. The algorithm decides differently based on the learner’s past experiences, which makes this method both adaptive to individuals and specific to each individual piece of content."

To sum up, the research project is about estimating when the best time to review is. The tradeoff is not wanting to review something too many times too often, while at the same time, wanting to practice something enough times with appropriate spacing so it is permanently remembered. "Our algorithm takes up these two prerequisites and comes up with an optimal learning strategy."