Box Thirding: Anytime Best Arm Identification under Insufficient Sampling

2026-02-20

AI Summary

This work proposes the Box Thirding (B3) algorithm to address the challenge of efficiently identifying the optimal arm in large-scale action spaces under a fixed budget and insufficient sampling. B3 introduces, for the first time, a ternary comparison mechanism into fixed-budget best-arm identification, iteratively retaining the strongest arm, deferring the median arm, and eliminating the weakest arm—enabling anytime decision-making without prior knowledge of the total budget. By integrating random subset sampling with a dynamic arm filtering strategy, B3 achieves both theoretical guarantees and computational efficiency without requiring prior information on the total number of samples. Empirical results demonstrate that B3 significantly outperforms existing methods in terms of simple regret under limited budgets and validates its effectiveness on the New Yorker cartoon caption contest dataset.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Best Arm Identification
• Fixed-budget
• Anytime Algorithm
• Insufficient Sampling
• Large-scale Bandits

Innovation

• Best Arm Identification
• Anytime Algorithm
• Fixed-Budget
• Ternary Comparison
• Simple Regret