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arXiv · 2211.10293

Dueling Bandits: From Two-dueling to Multi-dueling

Yihan Du·Siwei Wang·Longbo Huang
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Abstract

We study a general multi-dueling bandit problem, where an agent compares multiple options simultaneously and aims to minimize the regret due to selecting suboptimal arms. This setting generalizes the traditional two-dueling bandit problem and finds many real-world applications involving subjective feedback on multiple options. We start with the two-dueling bandit setting and propose two efficient algorithms, DoublerBAI and MultiSBM-Feedback. DoublerBAI provides a generic schema for translating known results on best arm identification algorithms to the dueling bandit problem, and achieves a regret bound of $O(\ln T)$. MultiSBM-Feedback not only has an optimal $O(\ln T)$ regret, but also reduces the constant factor by almost a half compared to benchmark results. Then, we consider the general multi-dueling case and develop an efficient algorithm MultiRUCB. Using a novel finite-time regret analysis for the general multi-dueling bandit problem, we show that MultiRUCB also achieves an $O(\ln T)$ regret bound and the bound tightens as the capacity of the comparison set increases. Based on both synthetic and real-world datasets, we empirically demonstrate that our algorithms outperform existing algorithms.

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Yihan Du, Siwei Wang, Longbo Huang. 2022-11-16. Dueling Bandits: From Two-dueling to Multi-dueling. https://arxiv.org/abs/2211.10293

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