Fun Maximizing Search, (Non) Instance Optimality, and Video Games for Parrots
arxiv(2024)
摘要
Computerized Adaptive Testing (CAT) measures an examinee's ability while
adapting to their level. Both too many questions and too many hard questions
can make a test frustrating. Are there some CAT algorithms which can be proven
to be theoretically better than others, and in which framework? We show that
slightly extending the traditional framework yields a partial order on CAT
algorithms. For uni-dimensional knowledge domains, we analyze the theoretical
performance of some old and new algorithms, and we prove that none of the
algorithms presented are instance optimal, conjecturing that no instance
optimal can exist for the CAT problem.
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