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Efficient Selection of Multiple Bandit Arms: Theory and Practice.
Shivaram
Kalyanakrishnan and Peter Stone.
In Proceedings of the Twenty-seventh
International Conference on Machine Learning (ICML), 2010.
[PDF]257.1kB [postscript]679.3kB
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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