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We study the problem of $K$-armed dueling bandit for both stochastic andadversarial environments, where the goal of the learner is to aggregateinformation through relative preferences of pair of decisions points queried inan online sequential manner. We first propose a novel reduction from any(general) dueling bandits to multi-armed bandits and despite the simplicity, itallows us to improve many existing results in dueling bandits. In particular,\emph{we give the first best-of-both world result for the dueling banditsregret minimization problem} -- a unified framework that is guaranteed toperform optimally for both stochastic and adversarial preferencessimultaneously. Moreover, our algorithm is also the first to achieve an optimal$O(\sum_{i = 1}^K \frac{\log T}{\Delta_i})$ regret bound against theCondorcet-winner benchmark, which scales optimally both in terms of thearm-size $K$ and the instance-specific suboptimality gaps $\{\Delta_i\}_{i =1}^K$. This resolves the long-standing problem of designing an instancewisegap-dependent order optimal regret algorithm for dueling bandits (with matchinglower bounds up to small constant factors). We further justify the robustnessof our proposed algorithm by proving its optimal regret rate underadversarially corrupted preferences -- this outperforms the existingstate-of-the-art corrupted dueling results by a large margin. In summary, webelieve our reduction idea will find a broader scope in solving a diverse classof dueling bandits setting, which are otherwise studied separately frommulti-armed bandits with often more complex solutions and worse guarantees. Theefficacy of our proposed algorithms is empirically corroborated against theexisting dueling bandit methods.

Versatile Dueling Bandits: Best-of-both-World Analyses for Online Learning from Preferences