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

Efficient and Optimal Algorithms for Contextual Dueling Bandits under Realizability