We present a novel multilabel/ranking algorithm working in partial information settings. The algorithm is based on 2nd-order descent methods, and relies on upper-confidence bounds to trade-off exploration and exploitation. We analyze this algorithm in a partial adversarial setting, where covariates can be adversarial, but multilabel probabilities are ruled by (generalized) linear models. We show O(T~(12) log T) regret bounds, which improve in several ways on the existing results. We test the effectiveness of our upper-confidence scheme by contrasting against full-information baselines on real-world multilabel datasets, often obtaining comparable performance.
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