Optimal and Practical Batched Linear Bandit Algorithm

• URL: http://arxiv.org/abs/2507.08438v1
• Date: Fri, 11 Jul 2025 09:29:28 GMT
• Title: Optimal and Practical Batched Linear Bandit Algorithm
• Authors: Sanghoon Yu, Min-hwan Oh,
• Abstract summary: We study the linear bandit problem under limited adaptivity, known as the batched linear bandit.<n>We propose textttBLAE, a novel batched algorithm that integrates arm elimination with regularized G-optimal design.<n>Our analysis introduces new techniques for batch-wise optimal design and refined concentration bounds.
• Score: 8.087699764574788
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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 \texttt{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, \texttt{BLAE} demonstrates low computational overhead and strong empirical performance, outperforming state-of-the-art methods in extensive numerical evaluations. Thus, \texttt{BLAE} is the first algorithm to combine provable minimax-optimality in all regimes and practical superiority in batched linear bandits.

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