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

TL;DR

This paper presents a new algorithm for batched best arm identification in multi-armed bandits that reduces sample complexity and breaks previous batch size barriers, with extensions to linear bandits.

Contribution

The paper introduces a novel sample allocation scheme that improves batch efficiency and breaks the $ ext{log}(1/ riangle_2)$ barrier in batched best arm identification.

Findings

Achieves near-optimal sample complexity

Breaks the $ ext{log}(1/ riangle_2)$ barrier

Extends to linear bandits with similar improvements

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.