UniRank: Unimodal Bandit Algorithm for Online Ranking

International audience; We tackle, in the multiple-play bandit setting, the online ranking problem of assigning $L$ items to $K$ predefined positions on a web page in order to maximize the number of user clicks. We propose a generic algorithm, UniRank, that tackles state-of-the-art click models. The regret bound of this algorithm is a direct consequence of the unimodality-like property of the bandit setting with respect toa graph where nodes are ordered sets of indistinguishable items.The main contribution of UniRank is its $O\left(L/\Delta \log T\right)$ regret for $T$ consecutive assignments, where $\Delta$ relates to the reward-gap between two items.This regret bound is based on the usually implicit condition that two items may not have the same attractiveness.Experiments against state-of-the-art learning algorithms specialized or not for different click models, show that our method has better regret performance than other generic algorithms on real life and synthetic datasets.