基于图平滑性的推荐算法，用少量评分高效学习用户偏好。
Spectral bandits for smooth graph functions with applications in recommender systems
- 利用图上函数平滑性建模推荐系统，节点间相似度决定评分相似性。
- 仅需评估几十个节点，就能在数千项内容中准确估计用户偏好。
- 提出有效维度概念，算法复杂度随该维度线性增长，适合真实图结构。
图上的平滑函数在流形学习与半监督学习中有广泛应用。本文研究一种带宽问题，其中各动作的回报在图上平滑分布。该框架适用于涉及图结构的在线学习问题，如基于内容的推荐系统。每个推荐项目对应一个节点，其期望评分与其邻近节点相似。目标是推荐具有高期望评分的项目。我们设计的算法避免累积损失随节点数急剧上升。特别地，引入有效维度概念——在现实图中该值较小，并提出两种算法，其复杂度在该维度上呈线性增长。在真实内容推荐任务上的实验表明，仅通过评估数十个节点，即可对数千项内容的用户偏好进行良好估计。
原文摘要 · Abstract (English)
Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each recommended item is a node and its expected rating is similar to its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose two algorithms for solving our problem that scale linearly in this dimension. Our experiments on real-world content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens nodes evaluations.
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