  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^{1/2} 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.
