Who Will Purchase This Item Next? Reverse Next Period Recommendation in Grocery Shopping

In this article, we focus on a less studied item-centered task, where the recommender system is given an item and needs to identify users who are most likely to consume it. Examples of such item-centered tasks emerge when advertising products [37], reducing waste [51], or promoting a healthy lifestyle [34]. For example, if a supermarket wants to sell bread that will expire soon to reduce waste, then simply recommending the bread to all users will not only lead to high service costs, but it will also harm users’ experience for those who do not like bread. As a result, item-centered recommendation algorithms have to identify specific top-k users who have an interest and may consume a given item. We define a novel “item-centered” recommendation problem in a sequential setting, namely, reverse next-period recommendation (RNPR)¹:

Somewhat related to our item-centered focus, Wang et al. [46] have recently formulated the task of selecting potential “adopters” for a free-trial item to increase the exposure of the long-tail items. However, despite the similarity to our item-centered task, Wang et al. still focus on user-side performance.

While some previous studies have considered item-centered recommendation problems, their focus has typically been on improving efficiency in this setting rather than designing recommendation algorithms tailored to the new item-centered setting. Two related approaches that focus on efficiency are reverse maximum inner product search [reverse k-MIPS, 1] and reverse top-k queries [40, 41, 56]. These approaches do not consider the temporal information and assume that the user and item representation vectors are known or can be pre-computed in advance. As a result, they are not able to handle the RNPR task effectively.

In this article, we are specifically interested in the grocery-shopping scenario, where historical interactions consist of baskets (multi-sets of items), for the following reasons: (i) the demand for item-centered recommendation is very clear in the grocery-shopping scenario, e.g., to help reduce food waste² or to promote healthy lifestyles³;(ii) repetition behavior and exploration behavior both appear in the grocery-shopping scenario, which allows us to understand the imbalance between repetition and exploration in the item-centered recommendation scenario. Specifically, we regard the next n baskets after the historical interactions to be “the next time period.” We consider three key aspects of the RNPR task in this work: (i) user-centered methods for item-centered tasks, (ii) repetition vs. exploration behavior of users, and (iii) efficiency.

The main contributions of our article are as follows:

The remainder of the article is organized as follows: We discuss related work in Section 2. Section 3 is devoted to formulated the reverse next-period recommendation problem. In Section 4, we analyze users’ repeat behavior. Then, in Section 5, we introduce the HIF for addressing the RNPR task. Methods for candidate filtering are introduced in Section 6. Our experimental setup is described in Section 7 and our experimental results in Section 8. We conclude in Section 9.

Sequential item recommendation tasks have been investigated for many years. The purpose of such tasks is to consider users and their preferences and to recommend the next item according to those preferences. Recurrent neural networks (RNNs) [8, 15] and transformers [39] have shown strong performance in modeling sequential information, and they have been widely used to learn representations of historical behavior in session-based recommendation. GRU4Rec [14] leverages GRUs to model user sequences and then optimize a ranking-based loss for session-based recommendation. An updated version, GRURec+ [13], has a new ranking loss and sampling strategy. NARM [24] couples a GRU with an attention mechanism to make the recommendation model focus more on recent baskets. SASRec [20] employs a self-attention-based method to capture the temporal dynamics of sequential recommendations in an efficient way.

In addition to RNN- and transformer-based models, several deep learning techniques have been applied to this area. Memory networks are applied by STAMP [28] to capture a user’s general interests and current interests. SR-GNN [49] models a session sequence as a graph and then uses a graph neural network [33] to capture item transactions and learn an accurate item embedding. Tang and Wang [38] propose a CNN-based method to capture general interests and sequential patterns via vertical and horizontal filtering. Yuan et al. [55] introduce a generative model to improve the performance. Pre-trained models (such as BERT) [35] and knowledge graphs are also being applied to user-centered recommendations [18, 48].

In grocery shopping, both the sequences of historical interactions and the output of recommendations are sets (or rather, multisets) of items, so-called baskets, and the next-basket recommendation (NBR) task is a user-centered sequential recommendation task that caters to this scenario. Over the years, many dedicated NBR methods have been proposed [25]. These include Markov chain (MC)-based methods [32, 44], deep learning-based methods [2, 4, 16, 22, 47, 53, 54], and frequency neighbor-based methods [11, 17]. An analysis conducted by Li et al. [25] assesses and evaluates the NBR performance from a new repetition and exploration perspective; their comparisons show that recommending repeat items (items that a user has interacted with previously) is an easier task than recommending explore items (items that a user has never interacted with before).

All of the sequential recommendation methods mentioned above focus on the user perspective, whereas we propose the reverse next-period recommendation (RNPR) problem that focuses on the item perspective.

Item-centered recommendations focus on the item perspective. That is, they aim to recommend suitable users for a given item that are likely to interact positively with it (i.e., purchase it in a grocery-shopping setting, listen to it in a music recommendation setting, download and read it in a book recommendation setting, etc.). Early proposals of item-centered recommendation date back at least to the so-called reverse top-k query problem [40, 41, 56]. Early publications on this problem typically consider Euclidean spaces with low-dimensional (often, around 5) user and item vectors.

In recent years, recommender systems have benefited from the development of deep learning techniques, which can construct high-dimensional representations and embeddings of users and items. For example, Amagata and Hara [1] propose reverse top-k maximum inner product search (reverse k-MIPS), which assumes that d-dimensional representations of users and items are obtained via matrix factorization [21]. Interestingly, previous work on item-centered recommendations only focuses on efficiency (i.e., on reducing the computational costs) rather than on improving the performance on the item-centered recommendation task. Furthermore, they do not consider temporal dependencies between historical items, which is a key aspect of the sequential recommendation task. Recently, Wang et al. [46] have formulated a user selection problem for free-trial items, which aims to increase item exposure and retain user-side performance.

Unlike previous work, we formulate the RNPR problem in a sequential setting. We aim to find users who will purchase a given item and focus on item-side performance. Moreover, we do not only focus on the efficiency aspect, but also try to improve the performance on the RNPR task.

Assume we have a set of users and a set of items, denoted as \(U = \lbrace u_1, u_2, \ldots , u_o\rbrace\) and \(I = \lbrace i_1 ,i_2, \ldots , i_m\rbrace\), respectively. Each item belongs to a category \(c\in C = \lbrace c_1, c_2, \dots , c_q\rbrace\). \(B_u^t\) denotes user u’s basket at timestep t, where \(B_u^t\) consists of a set of items \(i\in {I}\). \(S_u^h = \lbrace B_u^1, B_u^2, \ldots , B_u^t\rbrace\) represents the sequence of historical interactions for user u, and \(S_u^n = \lbrace B_u^{t+1}, B_u^{t+2}, \ldots , B_u^{t+n}\rbrace\) represents the sequence of the next n interactions for user u. Then, \(I_u^h = \lbrace i_1, i_2, \ldots , i_z\rbrace\) and \(I_u^n = \lbrace i_1, i_2, \ldots , i_e\rbrace\) represent the item set that user u has purchased before and will purchase in the next n baskets, i.e., next period, respectively. \(C_u^h = \lbrace c_1, c_2, \ldots , c_v\rbrace\) represents the category set in which user u has purchased items before, \(C_u^n = \lbrace c_1, c_2, \ldots , c_w\rbrace\) represents the category set in which user u will purchase items in the next n baskets.

Given a specific item i, the users in U can be divided into repeat users and explore users based on the historical interaction with the item i:

Similarly, given a specific category c, the users in U can also be divided as follows:

Given a specific item i and historical interactions \(S^h=\lbrace S_1^h, S_2^h, \ldots , S_m^h\rbrace\) of target users \(u_1, \ldots , u_m\in U_i^t\), the goal of the reverse next-period recommendation (RNPR) task is to predict the top-k users \(P_i^n\subseteq U_i^t\), who will purchase the given item i in one of the next n baskets. To address the RNPR task, we seek to define a function f that takes item i and historical interactions \(S^h=\lbrace S_1^h, S_2^h, \ldots , S_m^h\rbrace\) of target users \(u_1, \ldots , u_m\) as input and returns \(P^n_i\):where \(P_i^n\) is a predicted ranked list, which contains top-k users for item i. Considering the difference types of users that we have defined above, we define three sub-tasks for RNPR:

Given a specific item i and its target users \(U_i^t\) for the RNPR task, the goal of candidate filtering is to select a subset of candidate users \(\hat{U}_i^t\subseteq U_i^t\) based on their historical interactions \(S^h\). More formally, we seek to define a candidate filtering function g such thatGiven a filtered set of candidate users \(\hat{U}_i^t\) for item i, we only compute item scores for users in this filtered set of users \(\hat{U}_i^t\) instead of all candidate users \(U_i^t\).

The objective of a user-centered recommendation model is to rank positive items higher than the negative items, i.e., giving a higher prediction score to positive items, where the prediction score for an item may not represent the user’s absolute preference on this item, as this prediction score can be influenced by other items in the catalog and the item distribution in the dataset, e.g., popularity. User-centered recommendation models usually only take a user.s historical interactions and learn the general interest of the user, but may not track the users. interest w.r.t. a specific given item as time goes by. To achieve accurate item-centered recommendations, there are two things that should be taken into consideration: (i) the prediction of the model should be appropriate and meaningful for ranking users for a given item; and (ii) apart from a user’s historical interactions, the recommendation model should also take the given item as input and be able to track user’s interests or habits w.r.t. the given item as time goes by.

The task of Rep-RNPR is to help a given item find repeat users. Different from explore users, repeat users have previously had direct interactions with the item that we want to recommend. Therefore, we employ a simple time-aware frequency model, which only uses users’ direct interactions with the given item instead of using item-item correlations and complex representations. Formally,where \(F_{u, i, j}\) denotes the user’s u purchase frequency of item i at timestamp j, \(\beta\) denotes the time-decay factor, which emphasizes the impact of recent interactions. We find the optimal \(\beta\) based on the historical data.

Different from the Expl-RNPR task in Section 5.1 and the Rep-RNPR task in Section 5.2, the Mixed-RNPR task considers both repeat users and explore users for the items that are to be recommended. Theoretically, a model for Expl-RNPR can also be applied to Mixed-RNPR without excluding repeat users in the final prediction stage. A recent analysis [25] shows that the repetition and exploration tasks in the (user-centered) NBR problem have different levels of difficulty, where the repetition task, i.e., recommending repeat items to a user, is a much easier task. In an item-centered recommendation scenario, we mainly use item-to-item relations to infer explore users’ interests for the target item, since explore users do not have any previous interactions with it. Yet, we can address repeat users prediction via the users’ direct interactions with the target item.

Considering the above differences between the repetition and exploration tasks in Mixed-RNPR, we propose a repetition-exploration user ranking(REUR) algorithm to decouple the two tasks and investigate the tradeoff between repetition and exploration in an item-centered setting. Specifically, as is shown in Algorithm 1, we use separate models for the repetition and exploration tasks.⁶ Note that the models designed in Section 5.1 and Section 5.2 can be used for ranking explore users and ranking repeat users, respectively. For a given item, we rank repeat users and explore users according to the scores derived from the repetition model \(M^\mathit {rep}\) and exploration model \(M^\mathit {expl}\), respectively. Then, REUR generates the final ranked list of users \(P^n_i\) by combining the above two ranked lists. We define a combination (repeat) ratio \(\alpha\), which controls the proportions of repeat users and explore users. Assume that we want to recommend a given item to k users. Then, REUR first selects the top-m highest-score repeat users and then fills any remaining slots with the top-n highest-scoring explore users, where \(m=k\cdot \alpha\) and \(n=k-m\).

As we will see, one simple way to achieve good performance on the Mixed-RNPR task is to find a global optimal combination ratio \(\alpha\) for all items. We notice that different items might have different repurchase tendencies, i.e., the repurchase tendency of a pan is likely to be smaller than that of the milk that is cooked in it, which might influence the optimal combination ratio. The repurchase tendency is defined by:We also cluster items according to their repurchase tendency \(RT_i\in [0, 0.2)\), \([0.2, 0.4)\), \([0.4, 0.6)\), \([0.6, 0.8)\), \([0.8, 1.0]\), and try to find the optimal combination ratio \(\alpha\) for each cluster. We sweep the combination ratio \(\alpha\) and select the optimal \(\alpha\) based on the performance of the validation set.

Apart from achieving good performance on the Mixed-RNPR task, another important task is to investigate the tradeoff between repetition and exploration to make sure that we gain an in-depth understanding of the potential imbalances in the RNPR task. With the REUR algorithm, we can also easily investigate the tradeoff by setting different combination ratios (see Section 8.4).

According to the repetition analysis in Section 4, users have regular habits in grocery shopping and category-level repetition behavior seems more stable and prominent than item-level repetition behavior. Next, we first propose two repetition rule-based candidate filtering methods, i.e., RRBF-item and RRBF-cat. Formally,

Repetition-rule based filtering (RRBF) does not consider the temporal information and is static. To further reduce the number of candidates on top of RRBF-cat, we propose a candidate filtering model (CFM) to predict whether a user likes to repurchase the category or not, then select the users who would like to purchase the category of the given item. The architecture of the candidate filtering model is shown in Figure 3. Note that the category catalog is relatively stable and small compared to the item catalog, and the items within the same category can share the same set of candidate users.

Candidate filtering model (CFM) predicts users’ repurchase behavior by modeling their dynamic demands within the target category. For the sake of simplicity, we do not consider dependencies among different categories. Specifically, we use the category-level repetition frequency vector \(\mathit {RepVec}\) of category \(c\in C\) (defined in Equation (15)), which contains both temporal information and frequency information.

Different categories might have different characteristics w.r.t. repurchase behavior. For example, daily necessities like fruit might be purchased during every visit to the grocery store, whereas users are less likely to repurchase household items like dish soap right after their previous purchase of dish soap. Therefore, we introduce a category-specific time-aware weight embedding \(\mathit {TW}_\mathit {cf}^c\) to model temporal dependencies. In addition, we introduce a global time-aware weight embedding \(\mathit {TW}_\mathit {cf}^g\) that can be shared and trained by all categories, so different categories can benefit from the training samples of each other. Given a use u and a category c, we first derive the category-specific repetition feature \(\mathit {RepF}^c_{u, c}\) and the general repetition feature \(\mathit {RepF}^g_{u, c}\), then we concat \(\mathit {RepF}^c_{u, c}\) and \(\mathit {RepF}^{g}_{u, c}\) with a category embedding \(\mathit {Emb}^c_{cf}\), and feed it to a two layer fully connected neural network, that is:where \(p_{u, c}\) is the probability that user u will purchase items within the category c; \(\oplus\) denotes the concatenation operation.

Once we obtain the repurchase probabilities \(p_{u, c}\) of the target users, we can set a filtering threshold \(\lambda\) to filter candidates. For a given item \(i \in I^c\), we only select users whose \(p_{u, c}\) is above the filtering threshold \(\lambda\) as candidates. The overall pipeline of Expl-RNPR is shown in Figure 3.

To better understand the RNPR problem and investigate the effectiveness of the proposed methods, we intend to answer the following questions through our experiments:

(RQ1) How do user-centered state-of-the-art NBR methods perform on the RNPR task? (RQ2) What is the effectiveness of our newly proposed methods? Do they outperform existing baselines? (RQ3) What is the effectiveness of our training strategies for the HIF model in Expl-RNPR? (RQ4) What are the differences and tradeoffs between the repetition and exploration tasks in Mixed-RNPR? (RQ5) Do the proposed candidate filtering strategies help to reduce computational costs at inference time? How does the candidate filtering process influence the performance of our models?

To ensure the reproducibility of our study, we conduct our experiments on two publicly available real-world datasets:

In each dataset, we sample active users with at least 30 baskets in the dataset and truncate a basket sequence to 100 baskets. We follow a strategy that is similar to the widely used leave-one-out approach to split the dataset. Specifically, for each user, the last 10 baskets are regarded as future baskets, and all remaining baskets are regarded as historical baskets. The statistics of the processed datasets are summarized in Table 4. All training is conducted using the historical data. We select target items according to their frequency in the ground-truth (a.k.a. future data) to ensure there are new users for this item in the next period, otherwise, we can only add zero to the evaluation metrics. Note that using the explore users’ frequency in the ground-truth instead of the repeat users’ not only allows us to address the Expl-RNPR task, but also to make a fair comparison between the Expl-RNPR task and the Mixed-RNPR task. Considering the number of users in each dataset, the minimum number of future new users’ for an item is set to 50 for the Instacart dataset, and 10 for the Dunnhumby dataset. Since we use category information in our model, splitting across items has a risk of information leakage. So, we split the items into validation and test dataset according to their corresponding category [11], 50% categories for validation, and 50% categories for testing. We repeat the split 5 times and report the average performance w.r.t. metrics over the 5 splits.

We construct three simple methods, i.e., Random, I-TopFreq, and C-TopFreq, two pre-training-based methods, i.e., Basket2Vec and User2Vec, and select three SOTA NBR methods according to References [25] and [2], i.e., DNNTSP [54], TIFUKNN [17], and ReCANet [2], as baseline methods for comparison:

To assess the performance of RNPR methods, we extend three widely used user-centered metrics to the item-centered setting and arrive at the following metrics: \(\mathit {Recall}@K\), \(\mathit {nDCG}@K,\) and \(\mathit {IHN}@K\).

\(\mathit {Recall}\) measures the ability to find all users who will purchase the given item in the next period:where \(P_{i_j}\) are the top-K predicted users for item \(i_j\), and \(T_{i_j}\) denotes ground-truth users for item \(i_j\).

\(\mathit {nDCG}\) is a ranking metric that also considers the order of the users:where \(p_k\) equals 1 if \(P_{i_j}^k\in T_{i_j}\), otherwise \(p_k=0\). \(P_{i_j}^k\) denotes the kth user in the predicted user list \(P_{i_j}\) for item \(i_j\).

\(\mathit {IHN}\) represents the average number of correct users the model can find for each item, that is:Since the two datasets that we use, Instacart and Dunnhumby, have different numbers of users, when we evaluate the Expl-RNPR and Mixed-RNPR performance, the value of K for the Instacart dataset is set to 100 and 200, the value of K for the Dunnhumby dataset is set to 50 and 100. Since the number of repeat user candidates is limited, the K is set to 20 and 50 for Rep-RNPR task.

For all experiments, we set the next period size to 5 and 10 baskets. For Basket2Vec and User2Vec the embedding size is set to 100 for all datasets. For TIFUKNN, the number of neighbors is selected from \([100, 200, 300,\) \(400, 500]\), the fusion weight and time-decay factor are selected from \([0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]\), and the window size is set to the next period size, i.e., 5 or 10.

DNNTSP and ReCANet are used with the same parameter settings as in References [54] and [2], respectively. For HIF, we use the same pre-trained item embeddings as Basket2Vec to make a fair comparison with it. For both the HIF model and CFM model, the hidden layer of the fully connected network is set to 32, the maximum user sequence is set to 30. For REUR, the time-decay factor \(\beta\) is chosen from \([0.5, 0.6, 0.7, 0.8, 0.9]\), we sweep the combination ratio \(\alpha\) in \([0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]\) to investigate the tradeoff and find the optimal \(\alpha\) for Mixed-RNPR. We use Adam optimizer with 0.001 as learning rate and 256 as batch size to train our models.

We use PyTorch to implement our model and train it using a TITAN X GPU with 12 G memory. We repeat our experiments five times and report the average results. The code for the HIF model and CFM model is based on PyTorch,¹² and we share the code and parameters in a public GitHub repository.¹³

Tables 5, 6, and 7 show the performance of all approaches for the Expl-RNPR task, Rep-RNPR task and the Mixed-RNPR task, respectively. We have several findings based on the experimental results. As expected, the performance of Random is always among the lowest in terms of all metrics for all tasks, as it just randomly selects users. C-TopFreq outperforms Random on the Expl-RNPR task, since it models users’ interests w.r.t. the category of the target item. I-TopFreq achieves competitive or even better performance compared to other approaches on both the Rep-RNPR and Mixed-RNPR task, which confirms that item repetition frequency information is important and only considering repeat users can achieve quite good performance on the Mixed-RNPR task.

Among the two pre-training based methods, Basket2Vec always achieves better performance than User2Vec in all cases, which indicates that basket-level pre-training can get better item representations than user-level pre-training. We suspect that this is because users’ interests are dynamic and items purchased at the same time have more similarity. Basket2Vec is the best performing approach on the Expl-RNPR task, but Basket2Vec is inferior to I-TopFreq on both the Rep-RNPR and Mixed-RNPR task, which suggests that the item-item correlation is less important than the item repetition frequency information in these two tasks.

Surprisingly, the state-of-the-art DNNTSP method performs poorly on the Expl-RNPR task; its performance is in the same range as that of Random. DNNTSP is supposed to capture item-item correlations effectively, as it leverages advanced techniques, i.e., a GNN and self-attention mechanism. The ReCANet method achieves quite good performance on the Rep-RNPR task and the Mixed-RNPR task, which further emphasizes the importance of modeling repeat users in the Mixed-RNPR task. However, ReCANet does not outperform the SimpleTF method w.r.t. these two item-centered tasks. A plausible reason is that the user-wise binary cross entropy loss tries to distinguish items for a given user, which is sub-optimal for “item-centered” recommendations, where the goal is to distinguish users for a given item. Compared to DNNTSP, the relatively simple TIFUKNN is more robust on the Expl-RNPR task and even achieves the best performance (among the baselines) on the Dunnhumby dataset and the second best performance on the Instacart dataset. For the Rep-RNPR task and Mixed-RNPR task, TIFUKNN achieves good performance on the Instacart dataset, as it adopts personal item frequency information. However, it performs worse than the simple I-TopFreq on Dunnhumby; we suspect that the underlying reason is that the KNN module has a negative impact on finding repeat users in the Rep-RNPR task and Mixed-RNPR task.

To sum up, the performance of the state-of-the-art NBR methods does not always generalize to the Expl-RNPR task, and they are overly complex for the Rep-RNPR task and the Mixed-RNPR task.

For the Expl-RNPR task, the performance of the HIF model is shown in Table 5 and Figure 4(a). We can make two main observations based on the results. First, HIF with average pooling strategy (HIF-mean) significantly outperforms all existing approaches on both datasets across all metrics, with improvements ranging from 14.4% to 35.7%, since HIF models users’ interests via item-item correlations and models habits via frequency information at the same time.¹⁴ Second, the performance of HIF is different when using different basket pooling strategies, and the average pooling strategy has a clear advantage over the max pooling strategy on both datasets. This result indicates that the average pooling retains more useful information and leads to better basket representations in the HIF model.

For the Rep-RNPR task, the performance of SimpleTF is shown in Table 6.¹⁵ Surprisingly, the SimpleTF method outperforms many complex neural/representation-based methods, with improvements ranging from 1.8% to 6.3%. This result indicates that not all user-centered techniques, e.g., learning item representations and leveraging neighbor information, are helpful in the item-centered recommendation setting.

For the Mixed-RNPR task, the performance of REUR is shown in Table 7 and Figure 4(b). REUR achieves the best performance on both datasets through the combination of repeat users ranking (derived from a simple time-aware frequency model) and explore users ranking (derived from the HIF model). The improvements range from 3.1% to 8.2% over the best baseline methods. Besides achieving the best performance, an important advantage of the REUR algorithm is that we can explicitly investigate the tradeoff between repetition and exploration, which will be discussed in Section 8.4. Note that REUR decouples repetition and exploration, which allows it to benefit from the candidate filtering part by only considering repeat users, which we will discuss later in Section 8.5.3.

To sum up, the HIF model, SimpleTF model, and REUR algorithm are the state-of-the-art methods on the Expl-RNPR, Rep-RNPR, and Mixed-RNPR tasks, respectively.

To analyze the effectiveness of our proposed training strategies and components, we conduct an ablation study on the two datasets. Specifically, we compare the performance of the full HIF model with the following four settings:

The results of the ablation study are shown in Table 8. The results show that both the habits capturing module and two strategies are beneficial for the HIF, because removing any of them will lead to a decrease in performance. Without habits module, the performance of HIF decreases, ranging from 5% to 20%, which indicates that the frequency information is valuable and the designed habits module is able to leverage this information to model users’ shopping habits. Furthermore, HIF w/o hab still outperforms the Basket2Vec baseline (in Table 5), which indicates that the interest module of HIF can capture users’ dynamic interests by modeling the dynamic user preferences.

When we employ the positive augmentation strategy, repeat users will be sampled and truncated for training. Without positive augmentation, the performance of HIF drops significantly on the Instacart dataset w.r.t. all metrics, ranging from 4.1% to 10.4%, while the drop is not significant in terms of several metrics, i.e., Recall@50, nDCG@50, and IHN@50, on the Dunnhumby dataset. A plausible reason for this result is that the Instacart dataset has more users to be ranked, which means that the Expl-RNPR task is more difficult on Instacart dataset, so HIF can benefit more from the augmented postive samples on the Instacart dataset but the original training samples are enough for finding the top-50 users on the Dunnhumby dataset. Training HIF without negative adjustment strategy results in 4.7% to 21.1% drops in performance. This indicates that avoiding the overlap between training input and prediction input is important and effective in training the HIF model for the Expl-RNPR task. Interestingly, training HIF without both sampling strategies (HIF w/o aug-pos and adj-neg) achieves better performance than training without negative adjustment strategy. The positive augmentation strategy can help us generate more positive samples, which means that the HIF model will also leverage more negative samples during training, and this will increase the probability of using the historical data of the ground-truth users. As a result, negative adjustment is especially important when using positive augmentation strategy, and HIF w/o adj-neg is inferior to other variants of HIF.

To investigate the tradeoff between repetition and exploration in the Mixed-RNPR task, we use the proposed REUR algorithm and sweep its combination (repeat) ratio \(\alpha\). Figure 5(a) shows the repetition and exploration tradeoff on different datasets when using the same combination ratio \(\alpha\). As the proportion of repeat users increases in the recommendation, the performance of REUR on the Mixed-RNPR task increases. REUR achieves its best performance when the combination ratio is 1.0, which indicates that REUR has more confidence in the last user in the repeat user ranking than in the first user in the explore user ranking. This suggests that the repetition task is much easier than the exploration task in the “item-centered” recommendation that we consider in this article.

As mentioned before, the repurchase tendency \(\mathit {RT}\) of an item can potentially influence the tradeoff. To further understand the repetition and exploration tradeoff, we also investigate this tradeoff on different groups items. To ensure there are enough items within the group, we explore three groups of items, i.e., \(\mathit {RT} \in [0, 0.2)\), \([0.2, 0.4)\), \([0.4, 0.6)\) on the Dunnhumby dataset and four groups \(RT \in [0, 0.2)\), \([0.2, 0.4)\), \([0.4, 0.6)\), \([0.6, 0.8)\) on the Instacart dataset. The results are shown in Figure 5(b). Interestingly, we observe the same trend in all groups of items, the performance increases when the repeat ratio \(\alpha\) increases, even in the group with a very low repurchase tendency, i.e., \(\mathit {RT}\in [0, 0.2)\). This result once again confirms the large gap in difficulty between the repetition task and the exploration task.

In this subsection, we first evaluate the effectiveness of candidate filtering and then discuss the influence on the Expl-RNPR task and insights on the Mixed-RNPR task.