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We consider the problem of ranking n experts based on their performances on dtasks. We make a monotonicity assumption stating that for each pair of experts,one outperforms the other on all tasks. We consider the sequential settingwhere in each round, the learner has access to noisy evaluations of activelychosen pair of expert-task, given the information available up to the actualround. Given a confidence parameter $\delta$ $\in$ (0, 1), we providestrategies allowing to recover the correct ranking of experts and develop abound on the total number of queries made by our algorithm that hold withprobability at least 1 -- $\delta$. We show that our strategy is adaptive tothe complexity of the problem (our bounds are instance dependent), and developmatching lower bounds up to a poly-logarithmic factor. Finally, we adapt ourstrategy to the relaxed problem of best expert identification and providenumerical simulation consistent with our theoretical results.

Active Ranking of Experts Based on their Performances in Many Tasks