Adversarial Multi-dueling Bandits
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911933266919424 |
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| author | Gajane, Pratik |
| author_facet | Gajane, Pratik |
| contents | We introduce the problem of regret minimization in adversarial multi-dueling bandits. While adversarial preferences have been studied in dueling bandits, they have not been explored in multi-dueling bandits. In this setting, the learner is required to select $m \geq 2$ arms at each round and observes as feedback the identity of the most preferred arm which is based on an arbitrary preference matrix chosen obliviously. We introduce a novel algorithm, MiDEX (Multi Dueling EXP3), to learn from such preference feedback that is assumed to be generated from a pairwise-subset choice model. We prove that the expected cumulative $T$-round regret of MiDEX compared to a Borda-winner from a set of $K$ arms is upper bounded by $O((K \log K)^{1/3} T^{2/3})$. Moreover, we prove a lower bound of $Ω(K^{1/3} T^{2/3})$ for the expected regret in this setting which demonstrates that our proposed algorithm is near-optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adversarial Multi-dueling Bandits Gajane, Pratik Machine Learning We introduce the problem of regret minimization in adversarial multi-dueling bandits. While adversarial preferences have been studied in dueling bandits, they have not been explored in multi-dueling bandits. In this setting, the learner is required to select $m \geq 2$ arms at each round and observes as feedback the identity of the most preferred arm which is based on an arbitrary preference matrix chosen obliviously. We introduce a novel algorithm, MiDEX (Multi Dueling EXP3), to learn from such preference feedback that is assumed to be generated from a pairwise-subset choice model. We prove that the expected cumulative $T$-round regret of MiDEX compared to a Borda-winner from a set of $K$ arms is upper bounded by $O((K \log K)^{1/3} T^{2/3})$. Moreover, we prove a lower bound of $Ω(K^{1/3} T^{2/3})$ for the expected regret in this setting which demonstrates that our proposed algorithm is near-optimal. |
| title | Adversarial Multi-dueling Bandits |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2406.12475 |