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arXiv · 2501.17370

Breaking the $\log(1/\Delta_2)$ Barrier: Better Batched Best Arm Identification with Adaptive Grids

Tianyuan Jin·Qin Zhang·Dongruo Zhou
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Abstract

We investigate the problem of batched best arm identification in multi-armed bandits, where we aim to identify the best arm from a set of $n$ arms while minimizing both the number of samples and batches. We introduce an algorithm that achieves near-optimal sample complexity and features an instance-sensitive batch complexity, which breaks the $\log(1/\Delta_2)$ barrier. The main contribution of our algorithm is a novel sample allocation scheme that effectively balances exploration and exploitation for batch sizes. Experimental results indicate that our approach is more batch-efficient across various setups. We also extend this framework to the problem of batched best arm identification in linear bandits and achieve similar improvements.

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Tianyuan Jin, Qin Zhang, Dongruo Zhou. 2025-01-29. Breaking the $\log(1/\Delta_2)$ Barrier: Better Batched Best Arm Identification with Adaptive Grids. https://arxiv.org/abs/2501.17370

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