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

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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2610.16840 [cs.LG]

(or arXiv:2610.16840v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.16840 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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