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.

翻译：本文提出Box Thirding（B3）算法，一种适用于固定预算约束下最优臂识别（BAI）的灵活高效算法。该算法专为任意时间BAI及大规模臂集场景设计，其中臂数量N过大，无法在有限预算T内完成穷举评估。算法采用迭代式三元比较：在每次迭代中，比较三个臂——对表现最佳的臂进行进一步探索，将中位性能臂推迟至后续比较，并淘汰最弱臂。即使在没有先验知识T的情况下，B3仍能达到与连续减半（SH）算法相当的ε-最优臂误识别概率，而后者需要将T作为预设参数应用于随机选择的c0个臂子集（该子集规模需适配预算约束）。在《纽约客》漫画标题竞赛数据集上的实验表明，在有限预算约束下，B3在简单遗憾指标上优于现有方法。