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), particularly in second language acquisition research (4⇓⇓–7). Moreover, 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 (less) time working on forgotten (recalled) information.
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.
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