We introduce the problem of regret minimization in Adversarial Dueling Bandits. As in classic Dueling Bandits, the learner has to repeatedly choose a pair of items and observe only a relative binary `win-loss’ feedback for this pair, but here this feedback is generated from an arbitrary preference matrix, possibly chosen adversarially. Our main result is an algorithm whose $T$-round regret compared to the \\emph{Borda-winner} from a set of $K$ items is $\\tilde{O}(K^{1\/3}T^{2\/3})$, as well as a matching $\\OmesdfsdfK^{1\/3}T^{2\/3})$ lower bound. We also prove a similar high probability regret bound. We further consider a simpler \\emph{fixed-gap} adversarial setup, which bridges between two extreme preference feedback models for dueling bandits: stationary preferences and an arbitrary sequence of preferences. For the fixed-gap adversarial setup we give an $\\smash{ \\tilde{O}((K\/\\Delta^2)\\log{T}) }$ regret algorithm, where $\\Delta$ is the gap in Borda scores between the best item and all other items, and show a lower bound of $\\OmesdfsdfK\/\\Delta^2)$ indicating that our dependence on the main problem parameters $K$ and $\\Delta$ is tight (up to logarithmic factors).<\/p>\n","protected":false},"excerpt":{"rendered":"
We introduce the problem of regret minimization in Adversarial Dueling Bandits. As in classic Dueling Bandits, the learner has to repeatedly choose a pair of items and observe only a relative binary `win-loss’ feedback for this pair, but here this feedback is generated from an arbitrary preference matrix, possibly chosen adversarially. Our main result is 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