Recommendation systems capable of providing diverse sets of results are a focus of increasing importance, with motivations ranging from fairness to novelty and other aspects of optimizing user experience. One form of diversity of recent interest is calibration, the notion that personalized recommendations should reflect the full distribution of a user's interests, rather than a single predominant category -- for instance, a user who mainly reads entertainment news but also wants to keep up with news on the environment and the economy would prefer to see a mixture of these genres, not solely entertainment news. Existing work has formulated calibration as a subset selection problem; this line of work observes that the formulation requires the unrealistic assumption that all recommended items receive equal consideration from the user, but leaves as an open question the more realistic setting in which user attention decays as they move down the list of results. In this paper, we consider calibration with decaying user attention under two different models. In both models, there is a set of underlying genres that items can belong to. In the first setting, where items are represented by fine-grained mixtures of genre percentages, we provide a $(1-1/e)$-approximation algorithm by extending techniques for constrained submodular optimization. In the second setting, where items are coarsely binned into a single genre each, we surpass the $(1-1/e)$ barrier imposed by submodular maximization and give a $2/3$-approximate greedy algorithm. Our work thus addresses the problem of capturing ordering effects due to decaying attention, allowing for the extension of near-optimal calibration from recommendation sets to recommendation lists.

翻译：推荐系统能够提供多样化结果集的能力日益重要，其动机涵盖公平性、新颖性及优化用户体验的其他方面。近期备受关注的一种多样性形式是校准，即个性化推荐应反映用户兴趣的完整分布，而非单一主导类别——例如，主要阅读娱乐新闻但同时也希望关注环境与经济新闻的用户，更倾向于看到这些类别的混合呈现，而非仅有娱乐新闻。现有研究将校准建模为子集选择问题；这类工作指出，该公式需要假设所有推荐项目获得用户同等关注，这在实际中难以成立，但更现实的设定——用户注意力在向下浏览结果列表时逐渐衰减——仍是一个开放问题。本文在两种不同模型下考虑具有注意力衰减特性的校准。在这两种模型中，项目可归属若干潜在类别。在第一种设定中，项目以细粒度的类别百分比混合表示，我们通过扩展约束子模优化技术，提出了一种(1-1/e)近似算法。在第二种设定中，项目被粗略归入单一类别，我们突破了子模最大化带来的(1-1/e)上界限制，给出了一种2/3近似的贪心算法。本工作解决了因注意力衰减而产生的排序效应问题，使近乎最优的校准可从推荐集合扩展到推荐列表。