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PAC Subset Selection in Stochastic Multi-armed Bandits.
Shivaram
Kalyanakrishnan, Ambuj Tewari, Peter
Auer, and Peter Stone.
In Proceedings of the 29th International Conference
on Machine Learning (ICML), pp. 655–662, Omnipress, New York, NY, USA, June-July 2012.
[PDF]230.2kB [postscript]519.5kB
We consider the problem of selecting, from among the arms of a stochastic $n$-armed bandit, a subset of size $m$ of those arms with the highest expected rewards, based on efficiently sampling the arms. This ``subset selection'' problem finds application in a variety of areas. In the authors' previous work \citepKalyanakrishnan+Stone:2010-bandit, this problem is framed under a PAC setting (denoted ``\textscExplore-$m$''), and corresponding sampling algorithms are analyzed. Whereas the formal analysis therein is restricted to the worst case sample complexity of algorithms, in this paper, we design and analyze an algorithm (``\textscLUCB'') with improved expected sample complexity. Interestingly \textscLUCB bears a close resemblance to the well-known \textscUCB algorithm for regret minimization. The expected sample complexity bound we show for \textscLUCB is novel even for single-arm selection (\textscExplore-$1$). We also give a lower bound on the worst case sample complexity of PAC algorithms for \textscExplore-$m$.
@InProceedings{ICML12-shivaram,
author = {Shivaram Kalyanakrishnan and Ambuj Tewari and Peter Auer and Peter Stone},
title = {{PAC} Subset Selection in Stochastic Multi-armed Bandits},
booktitle = {Proceedings of the 29th International Conference on Machine Learning (ICML)},
location = {Edinburgh, UK},
month = {June-July},
year = {2012},
abstract = {
We consider the problem of selecting, from among the arms of a stochastic $n$-armed bandit, a subset of size $m$ of those arms with the highest expected rewards, based on efficiently sampling the arms. This ``subset selection'' problem finds application in a variety of areas. In the authors' previous work~\citep{Kalyanakrishnan+Stone:2010-bandit}, this problem is framed under a PAC setting (denoted ``\textsc{Explore}-$m$''), and corresponding sampling algorithms are analyzed. Whereas the formal analysis therein is restricted to the worst case sample complexity of algorithms, in this paper, we design and analyze an algorithm (``\textsc{LUCB}'') with improved expected sample complexity. Interestingly \textsc{LUCB} bears a close resemblance to the well-known \textsc{UCB} algorithm for regret minimization. The expected sample complexity bound we show for \textsc{LUCB} is novel even for single-arm selection (\textsc{Explore}-$1$). We also give a lower bound on the worst case sample complexity of PAC algorithms for \textsc{Explore}-$m$.
},
ISBN = {978-1-4503-1285-1},
editor = {John Langford and Joelle Pineau},
publisher = {Omnipress},
address = {New York, NY, USA},
pages = {655--662},
}
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