  We consider the multi-label ranking approach to multi-label learning.
Boosting is a natural method for multi-label ranking as it aggregates weak
predictions through majority votes, which can be directly used as scores to
produce a ranking of the labels. We design online boosting algorithms with
provable loss bounds for multi-label ranking. We show that our first algorithm
is optimal in terms of the number of learners required to attain a desired
accuracy, but it requires knowledge of the edge of the weak learners. We also
design an adaptive algorithm that does not require this knowledge and is hence
more practical. Experimental results on real data sets demonstrate that our
algorithms are at least as good as existing batch boosting algorithms.
