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：能够提供多样化结果集的推荐系统正日益成为关注焦点，其动机涵盖公平性、新颖性以及优化用户体验的诸多方面。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型的混合内容，而非纯粹的娱乐新闻。现有研究将校准问题形式化为子集选择问题；这类研究指出该形式化要求所有推荐条目均获得用户同等关注这一不切实际的假设，但将用户注意力随结果列表下移而衰减这一更现实的设定作为开放问题留存。本文中，我们考虑在两种不同模型下具有衰减用户注意力的校准问题。两种模型均存在项目可归属的底层体裁集合。在第一种设定中，项目由精细化的体裁百分比混合表示，我们通过扩展约束子模优化技术，提出了$(1-1/e)$近似算法。在第二种设定中，项目被粗粒度地划分至单一体裁，我们突破了子模最大化所施加的$(1-1/e)$界限，给出了$2/3$近似的贪心算法。因此，我们的研究解决了因注意力衰减而产生的排序效应捕获问题，使得近似最优校准能够从推荐集合扩展至推荐列表。