Integrated recommendation, which aims at jointly recommending heterogeneous items from different channels in a main feed, has been widely applied to various online platforms. Though attractive, integrated recommendation requires the ranking methods to migrate from conventional user-item models to the new user-channel-item paradigm in order to better capture users' preferences on both item and channel levels. Moreover, practical feed recommendation systems usually impose exposure constraints on different channels to ensure user experience. This leads to greater difficulty in the joint ranking of heterogeneous items. In this paper, we investigate the integrated recommendation task with exposure constraints in practical recommender systems. Our contribution is forth-fold. First, we formulate this task as a binary online linear programming problem and propose a two-layer framework named Multi-channel Integrated Recommendation with Exposure Constraints (MIREC) to obtain the optimal solution. Second, we propose an efficient online allocation algorithm to determine the optimal exposure assignment of different channels from a global view of all user requests over the entire time horizon. We prove that this algorithm reaches the optimal point under a regret bound of $ \mathcal{O}(\sqrt{T}) $ with linear complexity. Third, we propose a series of collaborative models to determine the optimal layout of heterogeneous items at each user request. The joint modeling of user interests, cross-channel correlation, and page context in our models aligns more with the browsing nature of feed products than existing models. Finally, we conduct extensive experiments on both offline datasets and online A/B tests to verify the effectiveness of MIREC. The proposed framework has now been implemented on the homepage of Taobao to serve the main traffic.
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