Optimal and Practical Batched Linear Bandit Algorithm
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912532226113536 |
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| author | Yu, Sanghoon Oh, Min-hwan |
| author_facet | Yu, Sanghoon Oh, Min-hwan |
| contents | We study the linear bandit problem under limited adaptivity, known as the batched linear bandit. While existing approaches can achieve near-optimal regret in theory, they are often computationally prohibitive or underperform in practice. We propose BLAE, a novel batched algorithm that integrates arm elimination with regularized G-optimal design, achieving the minimax optimal regret (up to logarithmic factors in $T$) in both large-$K$ and small-$K$ regimes for the first time, while using only $O(\log\log T)$ batches. Our analysis introduces new techniques for batch-wise optimal design and refined concentration bounds. Crucially, BLAE demonstrates low computational overhead and strong empirical performance, outperforming state-of-the-art methods in extensive numerical evaluations. Thus, BLAE is the first algorithm to combine provable minimax-optimality in all regimes and practical superiority in batched linear bandits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08438 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal and Practical Batched Linear Bandit Algorithm Yu, Sanghoon Oh, Min-hwan Machine Learning We study the linear bandit problem under limited adaptivity, known as the batched linear bandit. While existing approaches can achieve near-optimal regret in theory, they are often computationally prohibitive or underperform in practice. We propose BLAE, a novel batched algorithm that integrates arm elimination with regularized G-optimal design, achieving the minimax optimal regret (up to logarithmic factors in $T$) in both large-$K$ and small-$K$ regimes for the first time, while using only $O(\log\log T)$ batches. Our analysis introduces new techniques for batch-wise optimal design and refined concentration bounds. Crucially, BLAE demonstrates low computational overhead and strong empirical performance, outperforming state-of-the-art methods in extensive numerical evaluations. Thus, BLAE is the first algorithm to combine provable minimax-optimality in all regimes and practical superiority in batched linear bandits. |
| title | Optimal and Practical Batched Linear Bandit Algorithm |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2507.08438 |