Regret Lower Bound and Optimal Algorithm in Dueling Bandit Problem

TL;DR

This paper establishes a fundamental lower bound for regret in the dueling bandit problem and introduces an optimal algorithm that matches this bound, demonstrating superior empirical performance.

Contribution

It provides the first tight asymptotic regret lower bound and proposes an algorithm that achieves this bound in the dueling bandit setting.

Findings

The proposed algorithm matches the regret lower bound.

Experimental results show the algorithm outperforms existing methods.

The lower bound is based on information divergence.

Abstract

We study the $K$-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. We introduce a tight asymptotic regret lower bound that is based on the information divergence. An algorithm that is inspired by the Deterministic Minimum Empirical Divergence algorithm (Honda and Takemura, 2010) is proposed, and its regret is analyzed. The proposed algorithm is found to be the first one with a regret upper bound that matches the lower bound. Experimental comparisons of dueling bandit algorithms show that the proposed algorithm significantly outperforms existing ones.