Near Optimal Non-asymptotic Sample Complexity of 1-Identification

TL;DR

This paper introduces a new algorithm for the 1-identification problem in multi-armed bandits, achieving near-optimal non-asymptotic sample complexity with theoretical guarantees and empirical validation.

Contribution

The paper presents the first non-asymptotic analysis for 1-identification, matching upper and lower bounds up to a logarithmic factor, and introduces the SEE algorithm.

Findings

Achieves near-optimal sample complexity bounds.

The SEE algorithm outperforms existing benchmarks.

Provides theoretical and empirical validation of the approach.

Abstract

Motivated by an open direction in existing literature, we study the 1-identification problem, a fundamental multi-armed bandit formulation on pure exploration. The goal is to determine whether there exists an arm whose mean reward is at least a known threshold $\mu_0$, or to output None if it believes such an arm does not exist. The agent needs to guarantee its output is correct with probability at least $1-\delta$. Degenne & Koolen 2019 has established the asymptotically tight sample complexity for the 1-identification problem, but they commented that the non-asymptotic analysis remains unclear. We design a new algorithm Sequential-Exploration-Exploitation (SEE), and conduct theoretical analysis from the non-asymptotic perspective. Novel to the literature, we achieve near optimality, in the sense of matching upper and lower bounds on the pulling complexity. The gap between the upper and lower bounds is up to a polynomial logarithmic factor. The numerical result also indicates the effectiveness of our algorithm, compared to existing benchmarks.