Adaptive Experiments Under High-Dimensional and Data Sparse Settings: Applications for Educational Platforms

In online educational platforms, adaptive experiment designs play a critical role in personalizing learning pathways, instructional sequencing, and content recommendations. Traditional adaptive policies, such as Thompson Sampling, struggle with scalability in high-dimensional and sparse settings such as when there are large amount of treatments (arms) and limited resources such as funding and time to conduct to a classroom constraint student size. Furthermore, the issue of under-exploration in large-scale educational interventions can lead to suboptimal learning recommendations. To address these challenges, we build upon the concept of lenient regret, which tolerates limited suboptimal selections to enhance exploratory learning, and propose a framework for determining the feasible number of treatments given a sample size. We illustrate these ideas with a case study in online educational learnersourcing examples, where adaptive algorithms dynamically allocate peer-crafted interventions to other students under active recall exercise. Our proposed Weighted Allocation Probability Adjusted Thompson Sampling (WAPTS) algorithm enhances the efficiency of treatment allocation by adjusting sampling weights to balance exploration and exploitation in data-sparse environments. We present comparative evaluations of WAPTS across various sample sizes (N=50, 300, 1000) and treatment conditions, demonstrating its ability to mitigate under-exploration while optimizing learning outcomes.