We investigate the problem of online collaborative filtering under no-repetition constraints, whereby users need to be served content in an online fashion and a given user cannot be recommended the same content item more than once. We start by designing and analyzing an algorithm that works under biclustering assumptions on the user-item preference matrix, and show that this algorithm exhibits an optimal regret guarantee, while being fully adaptive, in that it is oblivious to any prior knowledge about the sequence of users, the universe of items, as well as the biclustering parameters of the preference matrix. We then propose a more robust version of this algorithm which operates with general matrices. Also this algorithm is parameter free, and we prove regret guarantees that scale with the amount by which the preference matrix deviates from a biclustered structure. To our knowledge, these are the first results on online collaborative filtering that hold at this level of generality and adaptivity under no-repetition constraints. Finally, we complement our theoretical findings with simple experiments on real-world datasets aimed at both validating the theory and empirically comparing to standard baselines. This comparison shows the competitive advantage of our approach over these baselines.

翻译：我们研究了无重复约束下的在线协同过滤问题，其中用户需以在线方式接收内容推荐，且同一用户不得重复推荐相同内容项。首先，我们设计并分析了一种基于用户-物品偏好矩阵双聚类假设的算法，证明该算法在完全自适应（无需预知用户序列、物品集合及偏好矩阵双聚类参数等先验知识）条件下，具备最优遗憾界保证。随后，我们提出该算法的更鲁棒版本，使其可适用于一般矩阵。该版本同样无需预知参数，且我们证明其遗憾界与偏好矩阵偏离双聚类结构的程度成比例缩放。据我们所知，这是首个在无重复约束下实现如此通用性与自适应性的在线协同过滤理论结果。最后，我们通过在真实数据集上的简单实验补充理论发现，既验证理论的有效性，亦与标准基线方法进行实证比较。结果表明，我们的方法相较于这些基线具有竞争优势。