# BOBCAT: Bilevel Optimization-Based Computerized Adaptive Testing

arXiv: https://arxiv.org/abs/2108.07386 · HTML: https://mlsanity.com/paper/2108.07386/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 17 Aug 2021.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [EdNet: A Large-Scale Hierarchical Dataset in Education](https://mlsanity.com/paper/1912.03072/) (2019)
- [Neural Cognitive Diagnosis for Intelligent Education Systems](https://mlsanity.com/paper/1908.08733/) (2019)
- [Instructions and Guide for Diagnostic Questions: The NeurIPS 2020 Education Challenge](https://mlsanity.com/paper/2007.12061/) (2020)
- [Enhancing Item Response Theory for Cognitive Diagnosis](https://mlsanity.com/paper/1905.10957/) (2019)
- [Deep Reinforcement Learning for Adaptive Learning Systems](https://mlsanity.com/paper/2004.08410/) (2020)

## Built on by (most cited first, 22 of 22)

- [Raising the Bar: Investigating the Values of Large Language Models via Generative Evolving Testing](https://mlsanity.com/paper/2406.14230/) (2024)
- [Adapting Large Language Models for Education: Foundational Capabilities, Potentials, and Challenges](https://mlsanity.com/paper/2401.08664/) (2023)
- [Efficient Lifelong Model Evaluation in an Era of Rapid Progress](https://mlsanity.com/paper/2402.19472/) (2024)
- [A Survey of Models for Cognitive Diagnosis: New Developments and Future Directions](https://mlsanity.com/paper/2407.05458/) (2024)
- [Survey of Computerized Adaptive Testing: A Machine Learning Perspective](https://mlsanity.com/paper/2404.00712/) (2024)
- [Do We Fully Understand Students' Knowledge States? Identifying and Mitigating Answer Bias in Knowledge Tracing](https://mlsanity.com/paper/2308.07779/) (2023)
- [Click-Based Student Performance Prediction: A Clustering Guided Meta-Learning Approach](https://mlsanity.com/paper/2111.00901/) (2021)
- [Balancing Test Accuracy and Security in Computerized Adaptive Testing](https://mlsanity.com/paper/2305.18312/) (2023)
- [Reinforcement Learning Guided Multi-Objective Exam Paper Generation](https://mlsanity.com/paper/2303.01042/) (2023)
- [Addressing Selection Bias in Computerized Adaptive Testing: A User-Wise Aggregate Influence Function Approach](https://mlsanity.com/paper/2308.11912/) (2023)
- [Diffusion-Inspired Cold Start with Sufficient Prior in Computerized Adaptive Testing](https://mlsanity.com/paper/2411.12182/) (2024)
- [LLM4CD: Leveraging Large Language Models for Open-World Knowledge Augmented Cognitive Diagnosis](https://mlsanity.com/paper/2505.13492/) (2025)
- [DiPS: Differentiable Policy for Sketching in Recommender Systems](https://mlsanity.com/paper/2112.07616/) (2021)
- [Amortised Design Optimization for Item Response Theory](https://mlsanity.com/paper/2307.09891/) (2023)
- [TestAgent: An Adaptive and Intelligent Expert for Human Assessment](https://mlsanity.com/paper/2506.03032/) (2025)
- [PEOAT: Personalization-Guided Evolutionary Question Assembly for One-Shot Adaptive Testing](https://mlsanity.com/paper/2512.00439/) (2025)
- [CodeGENCAT: Generative Computerized Adaptive Testing for Open-ended Coding Problems](https://mlsanity.com/paper/2602.20020/) (2026)
- [Embedding Enhancement via Fine-Tuned Language Models for Learner-Item Cognitive Modeling](https://mlsanity.com/paper/2604.04088/) (2026)
- [MBP-KT: Learning Global Collaborative Information from Meta-Behavioral Pattern for Enhanced Knowledge Tracing](https://mlsanity.com/paper/2605.08697/) (2026)
- [AgentCAT: Simulating Computerized Adaptive Testing via Multi-Agent Large Language Models](https://mlsanity.com/paper/2606.21832/) (2026)
- [Archetypes or ability? Clustering for modelling student mathematical competence](https://mlsanity.com/paper/2607.26063/) (2026)
- [Hypothesis Testing with Conditional Queries: Learnability and the Value of Interaction](https://mlsanity.com/paper/2608.06262/) (2026)

## Abstract (arXiv)

Computerized adaptive testing (CAT) refers to a form of tests that are personalized to every student/test taker. CAT methods adaptively select the next most informative question/item for each student given their responses to previous questions, effectively reducing test length. Existing CAT methods use item response theory (IRT) models to relate student ability to their responses to questions and static question selection algorithms designed to reduce the ability estimation error as quickly as possible; therefore, these algorithms cannot improve by learning from large-scale student response data. In this paper, we propose BOBCAT, a Bilevel Optimization-Based framework for CAT to directly learn a data-driven question selection algorithm from training data. BOBCAT is agnostic to the underlying student response model and is computationally efficient during the adaptive testing process. Through extensive experiments on five real-world student response datasets, we show that BOBCAT outperforms existing CAT methods (sometimes significantly) at reducing test length.