UniRank: Unimodal Bandit Algorithms for Online Ranking
Camille-Sovanneary Gauthier, Romaric Gaudel, Elisa Fromont
Abstract
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 pseudo-unimodality 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/$\Delta$ logT) 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.
BibTeX
@InProceedings{pmlr-v162-gauthier22a,
title = {{U}ni{R}ank: Unimodal Bandit Algorithms for Online Ranking},
author = {Gauthier, Camille-Sovanneary and Gaudel, Romaric and Fromont, Elisa},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {7279--7309},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/gauthier22a/gauthier22a.pdf},
url = {https://proceedings.mlr.press/v162/gauthier22a.html},
abstract = {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 pseudo-unimodality 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/$\Delta$ logT) 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.}
}