## 1 Introduction
However, it still treats items equally, underemphasizing items that are more influential in set-based preference. Against the shortcomings of ignoring the different item importance  
Figure 1: The illustration of _set-based preference learning_ (SPL) problem settings. Users \(\mathcal{U}=\{u_{1},u_{2},u_{3}\}\) rate sets \(\mathcal{S}=\{s_{1},s_{2},s_{3}\}\), which contain items randomly picked from \(\mathcal{I}=\{i_{1},i_{2},\ldots,i_{10}\}\). The set ratings user \(u\) gives, set \(s\), are denoted as \(\hat{r}_{u}^{s}\). \(\hat{r}_{u}^{s}\) is the _predicted_ preference scores for user \(u\)’s ratings of set \(s\). The prediction process is optimized by minimizing the loss between \(\hat{r}_{u}^{s}\) and \(\hat{r}_{u}^{s}\). \(\hat{r}_{u}^{s}\) is aggregated from predicted item ratings in a personalized way. As the training process proceeds, the set-rating prediction becomes more accurate. As a by-product, we get more reasonable item-rating predictions. At this point, the goal of inferring user preference over individual items based on set-level feedback is achieved. in the above methods, the _extremal subset average rating model (ESARM)_ enumerates all extremal subsets of item predictions and aggregates these subsets via linear weighted sum. Although considering the different impact of items in set, extremal subset average rating model ignores the fact that the selection of subsets should be highly flexible to reflect personalized assessment strategies. Extremal subsets are not necessarily good choices for all users and items. Moreover, enumerating all extremal subsets causes a huge computation burden as the set size grows. The limitation of the these methods is that they are attempts at one-size-fits-all approaches to aggregate item-level predictions, thereby oversimplifying the interplay between items in aggregation. We argue that the user's rating of a set is largely influenced by subsets arousing the strongest emotional inclinations. For example, some users overrate a playlist because of a few songs that are highly favored; some users underrate the game bundle because of one very disliked game. Moreover, we believe that the influential subsets should be automatically selected in an end-to-end manner, instead of following a predefined rule. To these ends, we introduce a _self-attentive subset learning model_ (SaSLM), which predicts item-level preferences from set-based feedback by capturing the interrelation among items in the set. Due to the computational burden of enumerating all possible combinations, it is nontrivial to find the optimal subsets in a personal way [6; 7; 8]. Rather than exhaustion, we propose to explicitly learn a personalized subset selection strategy via a _policy network_. Given the complex correlation between items in the set-rating process, we introduce a self-attention module to make sure all set members are considered in subset selection. Furthermore, we introduce gumble softmax in avoidance of gradient vanishing caused by binary selection in model learning. Then, the selected subsets are aggregated by personalized positional weights, which is a group of parameters specially learned for each user. The weights can be seen as the reflection of a user's rating pattern towards sets. We summarize the contributions of this paper:  
* We propose a novel method, self-attentive subset learning model (SaSLM), to study the problem of set-based preference learning (SPL), which is important to efficiently reveal users' preferences towards items with indirect supervision and protect their privacy as well. To the best of our knowledge, this is the first work to tackle set-based preference learning problem in an end-to-end manner. * We introduce a policy network to select a representative subset for each item set. By this means, the extent to which users' preferences are influenced by different items is fully considered. Our proposed subset selection strategy is more flexible.