On Elimination Strategies for Bandit Fixed-Confidence Identification

TL;DR

This paper introduces an adaptive elimination strategy for bandit identification that combines the computational efficiency of elimination algorithms with the adaptiveness of fully adaptive methods, improving performance in complex settings.

Contribution

The authors propose a novel adaptive elimination approach that enhances existing strategies by integrating elimination into both stopping and sampling rules, applicable to complex combinatorial problems.

Findings

Elimination improves computational complexity in adaptive bandit algorithms.

The new method maintains or improves sample complexity compared to non-elimination strategies.

Experimental results show significant efficiency gains in linear bandit best-arm identification.

Abstract

Elimination algorithms for bandit identification, which prune the plausible correct answers sequentially until only one remains, are computationally convenient since they reduce the problem size over time. However, existing elimination strategies are often not fully adaptive (they update their sampling rule infrequently) and are not easy to extend to combinatorial settings, where the set of answers is exponentially large in the problem dimension. On the other hand, most existing fully-adaptive strategies to tackle general identification problems are computationally demanding since they repeatedly test the correctness of every answer, without ever reducing the problem size. We show that adaptive methods can be modified to use elimination in both their stopping and sampling rules, hence obtaining the best of these two worlds: the algorithms (1) remain fully adaptive, (2) suffer a sample complexity that is never worse of their non-elimination counterpart, and (3) provably eliminate certain wrong answers early. We confirm these benefits experimentally, where elimination improves significantly the computational complexity of adaptive methods on common tasks like best-arm identification in linear bandits.