Contextual Combinatorial Bandits with Probabilistically Triggered Arms
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866910703615475712 |
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| author | Liu, Xutong Zuo, Jinhang Wang, Siwei Lui, John C. S. Hajiesmaili, Mohammad Wierman, Adam Chen, Wei |
| author_facet | Liu, Xutong Zuo, Jinhang Wang, Siwei Lui, John C. S. Hajiesmaili, Mohammad Wierman, Adam Chen, Wei |
| contents | We study contextual combinatorial bandits with probabilistically triggered arms (C$^2$MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C$^2$-UCB-T algorithm and propose a novel analysis that achieves an $\tilde{O}(d\sqrt{KT})$ regret bound, removing a potentially exponentially large factor $O(1/p_{\min})$, where $d$ is the dimension of contexts, $p_{\min}$ is the minimum positive probability that any arm can be triggered, and batch-size $K$ is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC$^2$-UCB and derive a regret bound $\tilde{O}(d\sqrt{T})$, which is independent of the batch-size $K$. As a valuable by-product, our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C$^2$MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17110 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Contextual Combinatorial Bandits with Probabilistically Triggered Arms Liu, Xutong Zuo, Jinhang Wang, Siwei Lui, John C. S. Hajiesmaili, Mohammad Wierman, Adam Chen, Wei Machine Learning Artificial Intelligence We study contextual combinatorial bandits with probabilistically triggered arms (C$^2$MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C$^2$-UCB-T algorithm and propose a novel analysis that achieves an $\tilde{O}(d\sqrt{KT})$ regret bound, removing a potentially exponentially large factor $O(1/p_{\min})$, where $d$ is the dimension of contexts, $p_{\min}$ is the minimum positive probability that any arm can be triggered, and batch-size $K$ is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC$^2$-UCB and derive a regret bound $\tilde{O}(d\sqrt{T})$, which is independent of the batch-size $K$. As a valuable by-product, our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C$^2$MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets. |
| title | Contextual Combinatorial Bandits with Probabilistically Triggered Arms |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2303.17110 |