Robust Optimization of Personalized Learning Pathways Under Uncertainty in Student Performance

Abstract

Personalized learning systems have the potential to be more effective by designing the order of instruction for each learner, but the decisions are based on noisy measures of the performance of the learners. Inference of mastery probabilities from few interactions, varied engagement level, and imperfect measurements will be uncertain, and thus the optimal path generated might become ineffective due to the noise. In this paper, we propose a robust optimization approach for constructing personalized learning paths that maintain effectiveness under various performance realizations of the learners. Our proposed method considers the selection of personalized learning paths as a sequential decision problem with uncertain mastery-transition parameters, where uncertainty is represented usingbudgeted uncertainty sets, and then construct. The proposed model is structured in a three-step pipeline of: knowledge tracing for estimating the level of mastery and associated uncertainty, creating an uncertainty set based on those estimations, and robust optimization of the learning path considering the worst-case realization of that uncertainty set. We propose a chance-constrained variation that ensures a specific probability of fulfilling the constraints associated with the learning objectives. We utilize benchmark information on performance prediction and optimization of learning pathways from the existing literature to motivate the proposed framework, and a symbolic example will show how the robustness budget affects the suggested learning pathway.