Breaking the $\log(1/\Delta_2)$ Barrier: Better Batched Best Arm Identification with Adaptive Grids
Keywords: Bandits
Abstract: We investigate the problem of batched best arm identification in multi-armed bandits, where we want to find 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.
Primary Area: reinforcement learning
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Submission Number: 1407
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