## 1 Introduction  
Ubiquitous recommender systems provide effective solutions to improve users' experiences with online service platforms. Their main goal is to infer users' interests through their historical feedback information. Among the recommendation models applied, collaborative filtering (CF) approaches have demonstrated effective performance [1]. Most CF methods directly rely on the item-level feedback of users [2, 3], which causes privacy concerns, since the users' preferences towards individual items are private opinions. Moreover, this privacy risk potentially inhibits users from providing feedback in the first place. Thus, avoiding direct item-level preference exposure is reasonable in recommender systems [4]. We refer to the problem of understanding the user's preference for individual items by learning from set-level feedback as _set-based preference learning_ (SPL).The set-based feedback reveals users' preferences and naturally provides information hiding by blurring interactions with individual items. Thus, users are more willing to provide set-based feedback than item-level preferences. However, inferring item preference from set-based feedback is nontrivial. Since only set-based preference is provided, there is no direct supervision signal for item-level rating prediction. Therefore, the major challenge of SPL is _how to accurately infer a user's preferences for individual items based on set-level feedback_. Since only set ratings are provided as supervision signals, the item-level predictions should be aggregated as set-based preferences before being updated. Although a set consists of several items, set-based feedback cannot just be modeled by adding up item-level feedback, because it is also influenced by the implicit interplay between items [5]. For example, some users tend to give positive feedback as long as the set contains something that pipes their interest, whereas some users are inclined to underrate a set if it contains undesirable items. Moreover, users might not follow the same rating patterns when facing different sets. Set-rating behavior is also influenced by some specific items contained in the set. The interwind influence of item combinations varies from user to user, which complicates the problem even more. Considering the complex mutual influences of items in a set, the aggregation should be conducted in a personalized way. We illustrate the process of SPL in Figure 1. Set ratings are _what we have_, which will be used as a supervision signal in training. In order to optimize the model under the guidance of supervision signals, we need to predict users' ratings towards sets. To achieve this, we require two steps: **item preference prediction** and **personalized aggregation**. Predicted item ratings are aggregated in a personalized way to get set-level predictions. Predicted item ratings are _what we want_ eventually, but they can only be updated with indirect supervision. Item preference prediction has been fully explored in recent works, so the key of SPL comes down to personalized aggregation, which is _what we model_ in this work. Personalized aggregation aims to model the influence of item interplay for users, which is the main focus of solutions for SPL. Current works addressing the SPL problem focus on designing a personalized aggregation mechanism for item-level preference predictions. Since SPL is a less studied problem, there are only a few heuristic works addressing it, and the main difference between these existing models is how to aggregate the item-level predictions to get set-level predictions. The work in [5] proposed three algorithms of different intuitions. The _average rating model (ARM)_ takes an average of all item-level predictions to get set-level predictions. It assumes equal contributions of each item in the set, which ignores the impact of diverse preference of items in the set. The _variance offset average rating model (VOARM)_ considers the diversity of item-level predictions by adding a weighted variance term in aggregation.