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arXiv · 2610.16840

Few-for-Many Best-Arm Identification in Multi-Objective Bandits

Bo Xue·Yilu Liu·Haodong Jing·Hongzong Li·Xi Lin·Shuang Qiu
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Abstract

Real-world systems often serve many objectives but can deploy only a few options, whose performance must be learned from noisy feedback. Modeling each option as an arm in a multi-objective bandit, we introduce \emph{few-for-many best-arm identification}, which seeks a small set of arms minimizing the worst weighted degradation from the objective-wise optima, rather than the best arm for every objective. We consider both known objective groups and latent groups specified only by a representative budget, and propose \textsc{GFM-Elim} and \textsc{AFM-Elim} with instance-dependent sample-complexity guarantees. For Gaussian rewards, we further derive a lower bound for the latent-group setting and show that it is asymptotically attainable with high probability by an oracle-based Track-and-Stop procedure. Our results show that sharing observations across objectives and ignoring irrelevant objective-wise distinctions can substantially reduce the sampling cost, as confirmed by experiments on synthetic and real-world tasks.

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Bo Xue, Yilu Liu, Haodong Jing, Hongzong Li, Xi Lin, Shuang Qiu. 2026-10-12. Few-for-Many Best-Arm Identification in Multi-Objective Bandits. https://arxiv.org/abs/2610.16840

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