Efficient and Optimal Algorithms for Contextual Dueling Bandits under Realizability

TL;DR

This paper introduces a new, efficient algorithm for the $K$-armed contextual dueling bandit problem under realizability, achieving optimal regret rates and resolving an open problem in the field.

Contribution

It presents the first computationally efficient, regret-optimal algorithm for contextual dueling bandits under realizability, with a novel notion of best response regret.

Findings

Achieves the optimal regret rate for the new best response regret measure.

Runs in polynomial time assuming access to an online square loss regression oracle.

Resolves an open problem on oracle-efficient, regret-optimal algorithms for the problem.

Abstract

We study the $K$-armed contextual dueling bandit problem, a sequential decision making setting in which the learner uses contextual information to make two decisions, but only observes \emph{preference-based feedback} suggesting that one decision was better than the other. We focus on the regret minimization problem under realizability, where the feedback is generated by a pairwise preference matrix that is well-specified by a given function class $\mathcal F$. We provide a new algorithm that achieves the optimal regret rate for a new notion of best response regret, which is a strictly stronger performance measure than those considered in prior works. The algorithm is also computationally efficient, running in polynomial time assuming access to an online oracle for square loss regression over $\mathcal F$. This resolves an open problem of Dud\'ik et al. [2015] on oracle efficient, regret-optimal algorithms for contextual dueling bandits.