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Shivaram Kalyanakrishnan and Peter
Stone. **Efficient Selection of Multiple Bandit Arms: Theory and Practice**. In *Proceedings of the Twenty-seventh
International Conference on Machine Learning (ICML)*, 2010.

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We consider the general, widely applicable problem of selecting from $n$ real-valued random variables a subset of size $m$ of those with the highest means, based on as few samples as possible. This problem, which we denote \textscExplore-$m$, is a core aspect in several stochastic optimization algorithms, and applications of simulation and industrial engineering. The theoretical basis for our work is an extension of a previous formulation using multi-armed bandits that is devoted to identifying just the one best of $n$ random variables (\textscExplore-$1$). In addition to providing PAC bounds for the general case, we tailor our theoretically grounded approach to work efficiently in practice. Empirical comparisons of the resulting sampling algorithm against state-of-the-art subset selection strategies demonstrate significant gains in sample efficiency.

@InProceedings{ICML10-kalyanakrishnan, author = "Shivaram Kalyanakrishnan and Peter Stone", title = "Efficient Selection of Multiple Bandit Arms: Theory and Practice", booktitle = "Proceedings of the Twenty-seventh International Conference on Machine Learning (ICML)", year = "2010", abstract = { We consider the general, widely applicable problem of selecting from $n$ real-valued random variables a subset of size $m$ of those with the highest means, based on as few samples as possible. This problem, which we denote \textsc{Explore}-$m$, is a core aspect in several stochastic optimization algorithms, and applications of simulation and industrial engineering. The theoretical basis for our work is an extension of a previous formulation using multi-armed bandits that is devoted to identifying just the one best of $n$ random variables (\textsc{Explore}-$1$). In addition to providing PAC bounds for the general case, we tailor our theoretically grounded approach to work efficiently in practice. Empirical comparisons of the resulting sampling algorithm against state-of-the-art subset selection strategies demonstrate significant gains in sample efficiency. }, }

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