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Efficient Pure Exploration in Adaptive Round Model
Tianyuan Jin · Jieming SHI · Xiaokui Xiao · Enhong Chen

Tue Dec 10 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #21
In the adaptive setting, many multi-armed bandit applications allow the learner to adaptively draw samples and adjust sampling strategy in rounds. In many real applications, not only the query complexity but also the round complexity need to be optimized. In this paper, we study both PAC and exact top-$k$ arm identification problems and design efficient algorithms considering both round complexity and query complexity. For PAC problem, we achieve optimal query complexity and use only $O(\log_{\frac{k}{\delta}}^*(n))$ rounds, which matches the lower bound of round complexity, while most of existing works need $\Theta(\log \frac{n}{k})$ rounds. For exact top-$k$ arm identification, we improve the round complexity factor from $\log n$ to $\log_{\frac{1}{\delta}}^*(n)$, and achieve near optimal query complexity. In experiments, our algorithms conduct far fewer rounds, and outperform state of the art by orders of magnitude with respect to query cost.

Author Information

Tianyuan Jin (University of Science and Technology of China)
Xiaokui Xiao (National University of Singapore)
Enhong Chen (University of Science and Technology of China)

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