MAB Optimizer for Estimating Math Question Difficulty via Inverse CV without NLP

TL;DR

This paper presents APME, a reinforcement learning-based MAB framework that estimates question difficulty from solver performance data without NLP, improving adaptive assessment in symbolic domains.

Contribution

The study introduces a novel, domain-agnostic, self-supervised method for estimating question difficulty using inverse CV within a MAB framework, outperforming traditional models.

Findings

Achieved high accuracy with R2 of 0.9213 and RMSE of 0.0584 across datasets.

Outperformed regression, NLP, and IRT models in symbolic domains.

Highlighted the importance of variance in solver outcomes for difficulty estimation.

Abstract

The evolution of technology and education is driving the emergence of Intelligent & Autonomous Tutoring Systems (IATS), where objective and domain-agnostic methods for determining question difficulty are essential. Traditional human labeling is subjective, and existing NLP-based approaches fail in symbolic domains like algebra. This study introduces the Approach of Passive Measures among Educands (APME), a reinforcement learning-based Multi-Armed Bandit (MAB) framework that estimates difficulty solely from solver performance data -- marks obtained and time taken -- without requiring linguistic features or expert labels. By leveraging the inverse coefficient of variation as a risk-adjusted metric, the model provides an explainable and scalable mechanism for adaptive assessment. Empirical validation was conducted on three heterogeneous datasets. Across these diverse contexts, the model achieved an average R2 of 0.9213 and an average RMSE of 0.0584, confirming its robustness, accuracy, and adaptability to different educational levels and assessment formats. Compared with baseline approaches-such as regression-based, NLP-driven, and IRT models-the proposed framework consistently outperformed alternatives, particularly in purely symbolic domains. The findings highlight that (i) item heterogeneity strongly influences perceived difficulty, and (ii) variance in solver outcomes is as critical as mean performance for adaptive allocation. Pedagogically, the model aligns with Vygotskys Zone of Proximal Development by identifying tasks that balance challenge and attainability, supporting motivation while minimizing disengagement. This domain-agnostic, self-supervised approach advances difficulty tagging in IATS and can be extended beyond algebra wherever solver interaction data is available