Box Thirding: Anytime Best Arm Identification under Insufficient Sampling

Seohwa Hwang; Junyong Park

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arXiv · 2602.18186

Box Thirding: Anytime Best Arm Identification under Insufficient Sampling

Seohwa Hwang·Junyong Park

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Abstract

We introduce Box Thirding (B3), a flexible and efficient algorithm for Best Arm Identification (BAI) under fixed-budget constraints. It is designed for both anytime BAI and scenarios with large N, where the number of arms is too large for exhaustive evaluation within a limited budget T. The algorithm employs an iterative ternary comparison: in each iteration, three arms are compared--the best-performing arm is explored further, the median is deferred for future comparisons, and the weakest is discarded. Even without prior knowledge of T, B3 achieves an epsilon-best arm misidentification probability comparable to Successive Halving (SH), which requires T as a predefined parameter, applied to a randomly selected subset of c0 arms that fit within the budget. Empirical results show that B3 outperforms existing methods under limited-budget constraints in terms of simple regret, as demonstrated on the New Yorker Cartoon Caption Contest dataset.

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Seohwa Hwang, Junyong Park. 2026-02-20. Box Thirding: Anytime Best Arm Identification under Insufficient Sampling. https://arxiv.org/abs/2602.18186

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