Parametric Graph for Unimodal Ranking Bandit

We tackle the online ranking problem of assigning $L$ items to $K$ positions on a web page in order to maximize the number of user clicks. We propose an original algorithm, easy to implement and with strong theoretical guarantees to tackle this problem in the Position-Based Model (PBM) setting, well suited for applications where items are displayed on a grid. Besides learning to rank, our algorithm, GRAB (for parametric Graph for unimodal RAnking Bandit), also learns the parameter of a compact graph over permutations of $K$ items among $L$. The logarithmic regret bound of this algorithm is a direct consequence of the unimodality property of the bandit setting with respect to the learned graph. Experiments against state-of-the-art learning algorithms which also tackle the PBM setting, show that our method is more efficient while giving regret performance on par with the best known algorithms on simulated and real life datasets.