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Best-Arm Identification in Linear Bandits
[article]
<span title="2014-11-04">2014</span>
<i >
arXiv
</i>
<span class="release-stage" >pre-print</span>
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<span title="2014-09-22">2014</span>
<span class="release-stage" >pre-print</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1409.6110v1">arXiv:1409.6110v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qqa33ykyhzejljadxs5vwrmy6m">fatcat:qqa33ykyhzejljadxs5vwrmy6m</a> </span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1409.6110v1">arXiv:1409.6110v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qqa33ykyhzejljadxs5vwrmy6m">fatcat:qqa33ykyhzejljadxs5vwrmy6m</a> </span>
We study the best-arm identification problem in linear bandit, where the rewards of the arms depend linearly on an unknown parameter θ^* and the objective is to return the arm with the largest reward. We characterize the complexity of the problem and introduce sample allocation strategies that pull arms to identify the best arm with a fixed confidence, while minimizing the sample budget. In particular, we show the importance of exploiting the global linear structure to improve the estimate of
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<a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1409.6110v2">arXiv:1409.6110v2</a>
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... e reward of near-optimal arms. We analyze the proposed strategies and compare their empirical performance. Finally, as a by-product of our analysis, we point out the connection to the G-optimality criterion used in optimal experimental design.
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