Non-Asymptotic Analysis of a UCB-based Top Two Algorithm

A Top Two sampling rule for bandit identification is a method which selects the next arm to sample from among two candidate arms, a leader and a challenger. Due to their simplicity and good empirical performance, they have received increased attention in recent years. However, for fixed-confidence best arm identification, theoretical guarantees for Top Two methods have only been obtained in the asymptotic regime, when the error level vanishes. In this paper, we derive the first non-asymptotic upper bound on the expected sample complexity of a Top Two algorithm, which holds for any error level. Our analysis highlights sufficient properties for a regret minimization algorithm to be used as leader. These properties are satisfied by the UCB algorithm, and our proposed UCB-based Top Two algorithm simultaneously enjoys non-asymptotic guarantees and competitive empirical performance.