Open Problem: Tight Bounds for Kernelized Multi-Armed Bandits with Bernoulli Rewards
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914862617067520 |
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| author | Mussi, Marco Drago, Simone Metelli, Alberto Maria |
| author_facet | Mussi, Marco Drago, Simone Metelli, Alberto Maria |
| contents | We consider Kernelized Bandits (KBs) to optimize a function $f : \mathcal{X} \rightarrow [0,1]$ belonging to the Reproducing Kernel Hilbert Space (RKHS) $\mathcal{H}_k$. Mainstream works on kernelized bandits focus on a subgaussian noise model in which observations of the form $f(\mathbf{x}_t)+ε_t$, being $ε_t$ a subgaussian noise, are available (Chowdhury and Gopalan, 2017). Differently, we focus on the case in which we observe realizations $y_t \sim \text{Ber}(f(\mathbf{x}_t))$ sampled from a Bernoulli distribution with parameter $f(\mathbf{x}_t)$. While the Bernoulli model has been investigated successfully in multi-armed bandits (Garivier and Cappé, 2011), logistic bandits (Faury et al., 2022), bandits in metric spaces (Magureanu et al., 2014), it remains an open question whether tight results can be obtained for KBs. This paper aims to draw the attention of the online learning community to this open problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06321 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Open Problem: Tight Bounds for Kernelized Multi-Armed Bandits with Bernoulli Rewards Mussi, Marco Drago, Simone Metelli, Alberto Maria Machine Learning We consider Kernelized Bandits (KBs) to optimize a function $f : \mathcal{X} \rightarrow [0,1]$ belonging to the Reproducing Kernel Hilbert Space (RKHS) $\mathcal{H}_k$. Mainstream works on kernelized bandits focus on a subgaussian noise model in which observations of the form $f(\mathbf{x}_t)+ε_t$, being $ε_t$ a subgaussian noise, are available (Chowdhury and Gopalan, 2017). Differently, we focus on the case in which we observe realizations $y_t \sim \text{Ber}(f(\mathbf{x}_t))$ sampled from a Bernoulli distribution with parameter $f(\mathbf{x}_t)$. While the Bernoulli model has been investigated successfully in multi-armed bandits (Garivier and Cappé, 2011), logistic bandits (Faury et al., 2022), bandits in metric spaces (Magureanu et al., 2014), it remains an open question whether tight results can be obtained for KBs. This paper aims to draw the attention of the online learning community to this open problem. |
| title | Open Problem: Tight Bounds for Kernelized Multi-Armed Bandits with Bernoulli Rewards |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2407.06321 |