An adaptive learning system aims at providing instruction tailored to the current status of a learner, differing from the traditional classroom experience. The latest advances in technology make adaptive learning possible, which has the potential to provide students with high-quality learning benefit at a low cost. A key component of an adaptive learning system is a recommendation system, which recommends the next material (video lectures, practices, and so on, on different skills) to the learner, based on the psychometric assessment results and possibly other individual characteristics. An important question then follows: How should recommendations be made? To answer this question, a mathematical framework is proposed that characterizes the recommendation process as a Markov decision problem, for which decisions are made based on the current knowledge of the learner and that of the learning materials. In particular, two plain vanilla systems are introduced, for which the optimal recommendation at each stage can be obtained analytically.
Keywords: Gittins index; Markov decision process; adaptive learning; c-μ rule; hidden Markov model; multi-armed bandit problem; stochastic scheduling.