Notifications are important for the user experience in mobile apps and can influence their engagement. However, too many notifications can be disruptive for users. A typical mobile app usually has several types of notification, managed by distinct teams with objectives that are possibly conflicting with each other, or even with the overall platform objective. Therefore, there is a need for careful curation of notifications sent to users of these different types. In this work, we study a novel centralized approach for notification optimization, where we view the opportunities to send user notifications as items and types of notifications as buyers in an auction market. Furthermore, the auction setup is unique, and the platform has the ability to subsidize the bids from the notification types. Using tools from fair division, we study the application of competitive equilibrium for addressing this problem. We show that an Eisenberg-Gale-style convex program allows us to find an allocation that is fair to all notification types in hindsight. Using the dual of the formulation, we present an online algorithm that allocates notifications via first-price auctions using a pacing-multiplier approach. Secondly, we introduce an approach based on second-price auctions and pacing, which has the benefit of working well with existing advertising systems built for second-price auctions. Through an A/B test in production, we show that the second price-based auction system improves over a decentralized notification optimization system, leading to its launch in production for some Instagram notifications. Further, through simulations on Instagram notification data and a subsequent production A/B test, we compare the outcomes of first-price and second-price auctions and show that the former has more stable pacing multipliers.

翻译：通知对于移动应用中的用户体验至关重要，并能影响用户参与度。然而，过多的通知可能会对用户造成干扰。典型的移动应用通常有几种类型的通知，由不同团队管理，这些团队的目标可能相互冲突，甚至与整体平台目标相悖。因此，需要对发送给用户的不同类型通知进行精心策划。在本工作中，我们研究了一种新颖的集中式通知优化方法，将发送用户通知的机会视为拍卖市场中的物品，将通知类型视为买家。此外，该拍卖设置具有独特性，平台有能力补贴通知类型的出价。利用公平分配的工具，我们研究了竞争均衡在解决此问题中的应用。我们证明，Eisenberg-Gale风格的凸规划能够找到一种在事后对所有通知类型均公平的分配方案。通过该公式的对偶形式，我们提出了一种在线算法，该算法通过第一价格拍卖并使用节奏乘子方法来分配通知。其次，我们引入了一种基于第二价格拍卖和节奏的方法，其优点是与现有为第二价格拍卖构建的广告系统良好兼容。通过生产环境中的A/B测试，我们展示了基于第二价格的拍卖系统优于去中心化的通知优化系统，并因此被应用于部分Instagram通知的生产环境。此外，通过在Instagram通知数据上的模拟以及后续的生产环境A/B测试，我们比较了第一价格拍卖和第二价格拍卖的结果，并表明前者具有更稳定的节奏乘子。