Adversarial Bandits against Arbitrary Strategies
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866911284002291712 |
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| author | Kim, Jung-hun Yun, Se-Young |
| author_facet | Kim, Jung-hun Yun, Se-Young |
| contents | We study the adversarial bandit problem against arbitrary strategies, where the difficulty is captured by an unknown parameter $S$, which is the number of switches in the best arm in hindsight. To handle this problem, we adopt the master-base framework using the online mirror descent method (OMD). We first provide a master-base algorithm with simple OMD, achieving $\tilde{O}(S^{1/2}K^{1/3}T^{2/3})$, in which $T^{2/3}$ comes from the variance of loss estimators. To mitigate the impact of the variance, we propose using adaptive learning rates for OMD and achieve $\tilde{O}(\min\{\sqrt{SKTρ},S\sqrt{KT}\})$, where $ρ$ is a variance term for loss estimators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_14839 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Adversarial Bandits against Arbitrary Strategies Kim, Jung-hun Yun, Se-Young Machine Learning We study the adversarial bandit problem against arbitrary strategies, where the difficulty is captured by an unknown parameter $S$, which is the number of switches in the best arm in hindsight. To handle this problem, we adopt the master-base framework using the online mirror descent method (OMD). We first provide a master-base algorithm with simple OMD, achieving $\tilde{O}(S^{1/2}K^{1/3}T^{2/3})$, in which $T^{2/3}$ comes from the variance of loss estimators. To mitigate the impact of the variance, we propose using adaptive learning rates for OMD and achieve $\tilde{O}(\min\{\sqrt{SKTρ},S\sqrt{KT}\})$, where $ρ$ is a variance term for loss estimators. |
| title | Adversarial Bandits against Arbitrary Strategies |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2205.14839 |