A large number of online services provide automated recommendations to help users to navigate through a large collection of items. New items (products, videos, songs, advertisements) are suggested on the basis of the user's past history and --when available-- her demographic profile. Recommendations have to satisfy the dual goal of helping the user to explore the space of available items, while allowing the system to probe the user's preferences. We model this trade-off using linearly parametrized multi-armed bandits, propose a policy and prove upper and lower bounds on the cumulative "reward" that coincide up to constants in the data poor (high-dimensional) regime. Prior work on linear bandits has focused on the data rich (low-dimensional) regime and used cumulative "risk" as the figure of merit. For this data rich regime, we provide a simple modification for our policy that achieves near-optimal risk performance under more restrictive assumptions on the geometry of the problem. We test (a variation of) the scheme used for establishing achievability on the Netflix and MovieLens datasets and obtain good agreement with the qualitative predictions of the theory we develop.

该研究使用线性参数化多臂赌博机模型来提高在线服务推荐新产品、视频、歌曲和广告的效果，得到了能够满足用户喜好探索和系统数据调查的解决方案，并在Netflix和MovieLens数据集上进行了测试。

高维线性赌博机和推荐系统