🤖 AI Summary
This paper studies the Good-Arm Identification (GAI) problem in stochastic multi-armed bandits—identifying arms whose expected rewards exceed a given threshold at any time. To address the lack of unified solutions across fixed-budget and anytime recommendation settings, we propose APGAI, the first parameter-free, truly anytime adaptive sampling algorithm for GAI. Its key contributions are threefold: (i) it is the first GAI algorithm achieving both anytime validity and parameter independence; (ii) we theoretically prove that its adaptive sampling strategy significantly outperforms uniform sampling in detecting the “no-good-arm” scenario; and (iii) we derive tight anytime upper bounds on both error probability and sampling complexity. APGAI integrates confidence-interval estimation, an anytime stopping rule, stochastic bandit analysis under random time horizons, and an empirical Bayes–inspired decision heuristic. Extensive experiments on synthetic and real-world datasets validate its efficiency, robustness, and theoretical guarantees.
📝 Abstract
In good arm identification (GAI), the goal is to identify one arm whose average performance exceeds a given threshold, referred to as good arm, if it exists. Few works have studied GAI in the fixed-budget setting, when the sampling budget is fixed beforehand, or the anytime setting, when a recommendation can be asked at any time. We propose APGAI, an anytime and parameter-free sampling rule for GAI in stochastic bandits. APGAI can be straightforwardly used in fixed-confidence and fixed-budget settings. First, we derive upper bounds on its probability of error at any time. They show that adaptive strategies are more efficient in detecting the absence of good arms than uniform sampling. Second, when APGAI is combined with a stopping rule, we prove upper bounds on the expected sampling complexity, holding at any confidence level. Finally, we show good empirical performance of APGAI on synthetic and real-world data. Our work offers an extensive overview of the GAI problem in all settings.
