UniRank: Unimodal Bandit Algorithms for Online Ranking

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 to a graph where nodes are ordered sets of indistinguishable items. The main contribution of UniRank is its O (L/∆ log T ) regret for T consecutive assignments, where ∆ 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.