  We introduce a new model for online ranking in which the click probability
factors into an examination and attractiveness function and the attractiveness
function is a linear function of a feature vector and an unknown parameter.
Only relatively mild assumptions are made on the examination function. A novel
algorithm for this setup is analysed, showing that the dependence on the number
of items is replaced by a dependence on the dimension, allowing the new
algorithm to handle a large number of items. When reduced to the orthogonal
case, the regret of the algorithm improves on the state-of-the-art.
