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arXiv · 1710.06360

Good Arm Identification via Bandit Feedback

Hideaki Kano·Junya Honda·Kentaro Sakamaki·Kentaro Matsuura·Atsuyoshi Nakamura·Masashi Sugiyama
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Abstract

We consider a novel stochastic multi-armed bandit problem called {\em good arm identification} (GAI), where a good arm is defined as an arm with expected reward greater than or equal to a given threshold. GAI is a pure-exploration problem that a single agent repeats a process of outputting an arm as soon as it is identified as a good one before confirming the other arms are actually not good. The objective of GAI is to minimize the number of samples for each process. We find that GAI faces a new kind of dilemma, the {\em exploration-exploitation dilemma of confidence}, which is different difficulty from the best arm identification. As a result, an efficient design of algorithms for GAI is quite different from that for the best arm identification. We derive a lower bound on the sample complexity of GAI that is tight up to the logarithmic factor $\mathrm{O}(\log \frac{1}δ)$ for acceptance error rate $δ$. We also develop an algorithm whose sample complexity almost matches the lower bound. We also confirm experimentally that our proposed algorithm outperforms naive algorithms in synthetic settings based on a conventional bandit problem and clinical trial researches for rheumatoid arthritis.

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Hideaki Kano, Junya Honda, Kentaro Sakamaki, Kentaro Matsuura, Atsuyoshi Nakamura, Masashi Sugiyama. 2018-02-10. Good Arm Identification via Bandit Feedback. https://arxiv.org/abs/1710.06360

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