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Inducing Individual Students' Learning Strategies through Homomorphic POMDPs

Huifan Gao, Yifeng Zeng, Yinghui Pan

TL;DR

The paper tackles personalized ITS planning by relaxing the single-pattern assumption of standard POMDPs and introducing Homomorphic POMDPs (H-POMDPs) that share $S$, $A$, and $\\Omega$ while allowing multiple transition dynamics to capture diverse cognitive patterns. It develops an EM-based parameter learning framework to jointly infer pattern-specific $D,T,O$ and the membership weights $w_{i,j}$, with educational constraints to ensure plausible transitions and observations. Empirical evaluation on ASSISTments and QuanLang datasets shows that H-POMDPs improve student-performance prediction (ACC, AUC, MAE, RMSE) and enable more personalized learning strategies via IE-DP, particularly in domains with richer knowledge structures. The work demonstrates the potential of clustering cognitive patterns to enhance personalization in ITS and outlines future directions to scale the belief space and incorporate learning stereotypes.

Abstract

Optimizing students' learning strategies is a crucial component in intelligent tutoring systems. Previous research has demonstrated the effectiveness of devising personalized learning strategies for students by modelling their learning processes through partially observable Markov decision process (POMDP). However, the research holds the assumption that the student population adheres to a uniform cognitive pattern. While this assumption simplifies the POMDP modelling process, it evidently deviates from a real-world scenario, thus reducing the precision of inducing individual students' learning strategies. In this article, we propose the homomorphic POMDP (H-POMDP) model to accommodate multiple cognitive patterns and present the parameter learning approach to automatically construct the H-POMDP model. Based on the H-POMDP model, we are able to represent different cognitive patterns from the data and induce more personalized learning strategies for individual students. We conduct experiments to show that, in comparison to the general POMDP approach, the H-POMDP model demonstrates better precision when modelling mixed data from multiple cognitive patterns. Moreover, the learning strategies derived from H-POMDPs exhibit better personalization in the performance evaluation.

Inducing Individual Students' Learning Strategies through Homomorphic POMDPs

TL;DR

The paper tackles personalized ITS planning by relaxing the single-pattern assumption of standard POMDPs and introducing Homomorphic POMDPs (H-POMDPs) that share , , and while allowing multiple transition dynamics to capture diverse cognitive patterns. It develops an EM-based parameter learning framework to jointly infer pattern-specific and the membership weights , with educational constraints to ensure plausible transitions and observations. Empirical evaluation on ASSISTments and QuanLang datasets shows that H-POMDPs improve student-performance prediction (ACC, AUC, MAE, RMSE) and enable more personalized learning strategies via IE-DP, particularly in domains with richer knowledge structures. The work demonstrates the potential of clustering cognitive patterns to enhance personalization in ITS and outlines future directions to scale the belief space and incorporate learning stereotypes.

Abstract

Optimizing students' learning strategies is a crucial component in intelligent tutoring systems. Previous research has demonstrated the effectiveness of devising personalized learning strategies for students by modelling their learning processes through partially observable Markov decision process (POMDP). However, the research holds the assumption that the student population adheres to a uniform cognitive pattern. While this assumption simplifies the POMDP modelling process, it evidently deviates from a real-world scenario, thus reducing the precision of inducing individual students' learning strategies. In this article, we propose the homomorphic POMDP (H-POMDP) model to accommodate multiple cognitive patterns and present the parameter learning approach to automatically construct the H-POMDP model. Based on the H-POMDP model, we are able to represent different cognitive patterns from the data and induce more personalized learning strategies for individual students. We conduct experiments to show that, in comparison to the general POMDP approach, the H-POMDP model demonstrates better precision when modelling mixed data from multiple cognitive patterns. Moreover, the learning strategies derived from H-POMDPs exhibit better personalization in the performance evaluation.
Paper Structure (13 sections, 13 equations, 3 figures, 6 tables, 1 algorithm)

This paper contains 13 sections, 13 equations, 3 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The Homomorphic POMDP Modelling Approach
  3. Background Knowledge
  4. H-POMDP Specification
  5. H-POMDP Parameter Learning
  6. Simplification in the Parameter Learning
  7. Learning Strategy Induction
  8. Experimental Results
  9. Datasets on the Learning Activity
  10. Experiment 1: Evaluations on Students' Performance Prediction
  11. Experiment 2: Evaluations on Learning Strategy Induction
  12. Related Works
  13. Conclusion and Future Work

Figures (3)

  • Figure 1: A POMDP-based cognitive model that plans the practice-based learning over four time steps.
  • Figure 2: The H-POMDP parameter learning contains the procedures ($\rm a$-$\rm e$) where the sequences are clustered and the parameter values are updated simultaneously.
  • Figure 3: Knowledge concept structures of the four sub-datasets. The records of ASSIST1, ASSIST2 and ASSIST3 are from ASSIST, and the records of Quanlang1 are from QuanLang.

Theorems & Definitions (1)

  • Definition 1