  Most recommender systems recommend a list of items. The user examines the
list, from the first item to the last, and often chooses the first attractive
item and does not examine the rest. This type of user behavior can be modeled
by the cascade model. In this work, we study cascading bandits, an online
learning variant of the cascade model where the goal is to recommend $K$ most
attractive items from a large set of $L$ candidate items. We propose two
algorithms for solving this problem, which are based on the idea of linear
generalization. The key idea in our solutions is that we learn a predictor of
the attraction probabilities of items from their features, as opposing to
learning the attraction probability of each item independently as in the
existing work. This results in practical learning algorithms whose regret does
not depend on the number of items $L$. We bound the regret of one algorithm and
comprehensively evaluate the other on a range of recommendation problems. The
algorithm performs well and outperforms all baselines.
