Box Thirding: Anytime Best Arm Identification under Insufficient Sampling

TL;DR

Box Thirding (B3) is a novel algorithm for best arm identification that efficiently operates under fixed-budget constraints, especially suitable for large numbers of arms and anytime scenarios, with strong empirical performance.

Contribution

The paper introduces Box Thirding (B3), a new iterative ternary comparison algorithm for best arm identification that matches success probabilities of existing methods without prior knowledge of total budget.

Findings

B3 achieves comparable epsilon-best arm misidentification probability to Successive Halving.

Empirical results show B3 outperforms existing methods in simple regret under limited budgets.

B3 is effective for large N and anytime BAI scenarios.

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.