Minimum Empirical Divergence for Sub-Gaussian Linear Bandits
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912269014663168 |
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| author | Balagopalan, Kapilan Jun, Kwang-Sung |
| author_facet | Balagopalan, Kapilan Jun, Kwang-Sung |
| contents | We propose a novel linear bandit algorithm called LinMED (Linear Minimum Empirical Divergence), which is a linear extension of the MED algorithm that was originally designed for multi-armed bandits. LinMED is a randomized algorithm that admits a closed-form computation of the arm sampling probabilities, unlike the popular randomized algorithm called linear Thompson sampling. Such a feature proves useful for off-policy evaluation where the unbiased evaluation requires accurately computing the sampling probability. We prove that LinMED enjoys a near-optimal regret bound of $d\sqrt{n}$ up to logarithmic factors where $d$ is the dimension and $n$ is the time horizon. We further show that LinMED enjoys a $\frac{d^2}Δ\left(\log^2(n)\right)\log\left(\log(n)\right)$ problem-dependent regret where $Δ$ is the smallest sub-optimality gap. Our empirical study shows that LinMED has a competitive performance with the state-of-the-art algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_00229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimum Empirical Divergence for Sub-Gaussian Linear Bandits Balagopalan, Kapilan Jun, Kwang-Sung Machine Learning We propose a novel linear bandit algorithm called LinMED (Linear Minimum Empirical Divergence), which is a linear extension of the MED algorithm that was originally designed for multi-armed bandits. LinMED is a randomized algorithm that admits a closed-form computation of the arm sampling probabilities, unlike the popular randomized algorithm called linear Thompson sampling. Such a feature proves useful for off-policy evaluation where the unbiased evaluation requires accurately computing the sampling probability. We prove that LinMED enjoys a near-optimal regret bound of $d\sqrt{n}$ up to logarithmic factors where $d$ is the dimension and $n$ is the time horizon. We further show that LinMED enjoys a $\frac{d^2}Δ\left(\log^2(n)\right)\log\left(\log(n)\right)$ problem-dependent regret where $Δ$ is the smallest sub-optimality gap. Our empirical study shows that LinMED has a competitive performance with the state-of-the-art algorithms. |
| title | Minimum Empirical Divergence for Sub-Gaussian Linear Bandits |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2411.00229 |