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Hierarchical Multi-Armed Bandits for the Concurrent Intelligent Tutoring of Concepts and Problems of Varying Difficulty Levels

Blake Castleman, Uzay Macar, Ansaf Salleb-Aouissi

TL;DR

This work addresses the need for open-source, adaptive tutoring systems capable of concurrently steering learners through conceptual ideas and associated problems with varying difficulty. It proposes a deployable hierarchical MAB architecture consisting of a high-level concept MAB and a low-level problem MAB, guided by ZPDES and memory-decay modeling (MCM) and augmented with MAPLE-inspired transient difficulty ranking. Bayesian Knowledge Tracing simulations show that a difficulty-agnostic hierarchical MAB improves mastery, and adding problem difficulty adaptation yields additional gains, indicating practical benefits for remote education. By delivering an open-source platform and detailed parameterizations, the paper enables researchers and educators to implement and extend MAB-based tutoring pipelines in real-world settings, with future work focusing on real-world trials, dynamic difficulty updates, and material redirects for underperforming students.

Abstract

Remote education has proliferated in the twenty-first century, yielding rise to intelligent tutoring systems. In particular, research has found multi-armed bandit (MAB) intelligent tutors to have notable abilities in traversing the exploration-exploitation trade-off landscape for student problem recommendations. Prior literature, however, contains a significant lack of open-sourced MAB intelligent tutors, which impedes potential applications of these educational MAB recommendation systems. In this paper, we combine recent literature on MAB intelligent tutoring techniques into an open-sourced and simply deployable hierarchical MAB algorithm, capable of progressing students concurrently through concepts and problems, determining ideal recommended problem difficulties, and assessing latent memory decay. We evaluate our algorithm using simulated groups of 500 students, utilizing Bayesian Knowledge Tracing to estimate students' content mastery. Results suggest that our algorithm, when turned difficulty-agnostic, significantly boosts student success, and that the further addition of problem-difficulty adaptation notably improves this metric.

Hierarchical Multi-Armed Bandits for the Concurrent Intelligent Tutoring of Concepts and Problems of Varying Difficulty Levels

TL;DR

This work addresses the need for open-source, adaptive tutoring systems capable of concurrently steering learners through conceptual ideas and associated problems with varying difficulty. It proposes a deployable hierarchical MAB architecture consisting of a high-level concept MAB and a low-level problem MAB, guided by ZPDES and memory-decay modeling (MCM) and augmented with MAPLE-inspired transient difficulty ranking. Bayesian Knowledge Tracing simulations show that a difficulty-agnostic hierarchical MAB improves mastery, and adding problem difficulty adaptation yields additional gains, indicating practical benefits for remote education. By delivering an open-source platform and detailed parameterizations, the paper enables researchers and educators to implement and extend MAB-based tutoring pipelines in real-world settings, with future work focusing on real-world trials, dynamic difficulty updates, and material redirects for underperforming students.

Abstract

Remote education has proliferated in the twenty-first century, yielding rise to intelligent tutoring systems. In particular, research has found multi-armed bandit (MAB) intelligent tutors to have notable abilities in traversing the exploration-exploitation trade-off landscape for student problem recommendations. Prior literature, however, contains a significant lack of open-sourced MAB intelligent tutors, which impedes potential applications of these educational MAB recommendation systems. In this paper, we combine recent literature on MAB intelligent tutoring techniques into an open-sourced and simply deployable hierarchical MAB algorithm, capable of progressing students concurrently through concepts and problems, determining ideal recommended problem difficulties, and assessing latent memory decay. We evaluate our algorithm using simulated groups of 500 students, utilizing Bayesian Knowledge Tracing to estimate students' content mastery. Results suggest that our algorithm, when turned difficulty-agnostic, significantly boosts student success, and that the further addition of problem-difficulty adaptation notably improves this metric.
Paper Structure (24 sections, 8 equations, 3 figures, 1 algorithm)

This paper contains 24 sections, 8 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multi-Armed Bandit Intelligent Tutoring Frameworks - Without Difficulty Levels
  4. Multi-Armed Bandit Intelligent Tutoring Frameworks - With Difficulty Levels
  5. Methodology: Platform Architecture
  6. Platform Section, Concept, and Problem Definition
  7. Methodology: ZPDES Foundation for Algorithmic Progression
  8. ZPDES Multi-Armed Bandit Design Foundation
  9. MCM Algorithm Adaptation
  10. Methodology: High-Level Concept Multi-Armed Bandit
  11. Concept Progression Trees
  12. Problem Difficulty
  13. Methodology: Low-Level Problem Multi-Armed Bandit
  14. Problem Progression Trees
  15. Initial Problem Difficulty Integration
  16. ...and 9 more sections

Figures (3)

  • Figure 1: Progression tree examples for both the conceptual MAB and the problem MAB. Note that there are separate problem progression trees for each concept in a given section.
  • Figure 2: The average progression for groups of 500 simulated students' mastery of 5 sections (15 concepts) of material, using BKT. This includes a randomized sequence of questions (black), our hierarchical multi-armed bandit framework without problem difficulty considerations (red), and our hierarchical multi-armed bandit framework with problem difficulty included (blue).
  • Figure 3: A schematic of how the concept MAB and problem MABs interact.