An Anytime Algorithm for Good Arm Identification

2025-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

APGAI is a novel anytime and parameter-free sampling rule designed for Good Arm Identification (GAI) in stochastic bandit problems. GAI aims to identify an arm whose average performance surpasses a predefined threshold, if such an arm exists. While previous research on GAI has primarily focused on fixed-confidence settings, APGAI extends its applicability to both fixed-budget and anytime scenarios, allowing recommendations at any point. The algorithm's effectiveness is supported by derived upper bounds on its probability of error, demonstrating that adaptive strategies like APGAI can more efficiently detect the absence of good arms compared to uniform sampling across various instances. When integrated with a stopping rule, APGAI also exhibits strong upper bounds on expected sampling complexity, maintaining performance across different confidence levels. Empirical evaluations on synthetic and real-world datasets further validate APGAI's robust performance.

Key takeaway

For research scientists developing or deploying multi-armed bandit algorithms, APGAI provides a robust, parameter-free option for Good Arm Identification. You should consider integrating APGAI into systems requiring flexible, anytime recommendations or operating under fixed sampling budgets, as it offers provable performance guarantees and superior efficiency over uniform sampling.

Key insights

APGAI offers an adaptive, anytime, and parameter-free solution for Good Arm Identification in stochastic bandits.

Principles

• Adaptive strategies outperform uniform sampling.
• Anytime algorithms provide flexible recommendations.

Method

APGAI is a sampling rule for GAI in stochastic bandits. It adaptively samples arms, and when combined with a stopping rule, it provides bounds on sampling complexity and error probability at any time.

In practice

• Apply APGAI in fixed-budget GAI problems.
• Use APGAI for anytime recommendations in bandit settings.

Topics

• Good Arm Identification
• Anytime Algorithms
• Stochastic Bandits
• APGAI Algorithm
• Sampling Rules

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.