A receding-horizon estimation and control framework for the content sequencing problem

We propose a full receding-horizon approach to solve the problem of adaptively selecting the contents of a test while the test is being taken by a learner, while accounting for the past performance and the knowledge uptake needs of the learner itself. We thus present an approach that embeds a moving-horizon estimator to robustly infer the current knowledge levels of the learner, together with a model predictive controller to promote the robust selection of which items should be included in the test as it is being taken by the learner. Both receding-horizon algorithms are built on top of a model of the learners' knowledge uptake dynamics that accounts for Zone of Proximal Development effects, i.e., the hypothesis for which there exists an optimal difficulty level for the questions to maximize the learning at each step. We show that the proposed closed-loop approach outperforms the current policies that build tests either by randomly selecting questions within a database, or by making the difficulty of the questions nondecreasing as the test progresses.