Explicit Feature Interaction-aware Uplift Network for Online Marketing

Given a current marketing instance $z_{i}=(\bm{x}_{i},\bm{t}_{i},y_{i})$, unlike most existing works, we encode not only non-treatment features $\bm{x}_{i}$ but also treatment features $\bm{t}_{i}$ in this module. Taking the treatment feature as an example, for each continuous feature $t_{ij}$ in the treatment features, we equip it with a shared fully-connected network for encoding. For the remaining features in the treatment features, i.e., the sparse features, we initialize an embedding table for each feature and obtain the embedding representation corresponding to the specific feature value through the lookup operation. This encoding process can be expressed as,

where $\mathbf{W}_{j}$ is a weight matrix, $\mathbf{b}_{j}$ is a bias vector, and $\mathbf{E}_{j}$ is an embedding table. Intuitively, continuous features in treatment features are more likely to reflect the correlation between different treatments, such as similar amounts and minimum consumption to be satisfied, so the different encoding of continuous features in Eq.(3) aims to preserve this property. For non-treatment features, we adopt a similar encoding process. Finally, we can obtain the corresponding embedding representation, i.e., $\mathbf{e}^{x}_{i}=\{\mathbf{e}^{x}_{i0},\mathbf{e}^{x}_{i1},\dots,\mathbf{e}^{x}_{id_{x}}\}$ and $\mathbf{e}^{t}_{i}=\{\mathbf{e}^{t}_{i0},\mathbf{e}^{t}_{i1},\dots,\mathbf{e}^{t}_{id_{t}}\}$.

In this module, we use the embedding representation $\mathbf{e}^{x}_{i}$ to model the natural response of each user in the control group, where information about the treatment is isolated to capture user-sensitive features in the natural situation. We use a self-attention network for self-interaction to better predict natural responses. Specifically, we have,

where $K_{d}$ is the dimension of the output embedding, and $\mathbf{\overline{e}}^{x}_{i}=\{\mathbf{\overline{e}}^{x}_{i0},\mathbf{\overline{e}}^{x}_{i1},\dots,\mathbf{\overline{e}}^{x}_{id_{x}}\}$. Next, we use a multilayer perceptron to predict natural responses,

where $\mathbf{W}_{s}$ is a weight matrix and $\mathbf{b}_{s}$ is a bias vector. Based on the control group instances contained in the training set, the optimization objective of the self-interaction module is a supervised loss for natural responses,

In this module, we aim to use the embedding representations $\mathbf{e}^{x}_{i}$ and $\mathbf{e}^{t}_{i}$ to learn the responses of users in different treatment groups and to identify the corresponding sensitive features, where the treatment information will be used as inducements to achieve this goal. Note that this is different from the self-interaction module. Specifically, we first use a treatment-aware attention network to model the interaction between treatment features and non-treatment features, and use attention weights to describe the sensitivity of non-treatment features to a particular treatment,

where $\mathbf{W}_{t0}$, $\mathbf{W}_{t1}$ and $\mathbf{W}_{t2}$ are weight matrices and $\mathbf{b}_{t2}$ is a bias vector. Based on this embedded representation combined with interaction information, we then estimate the ITE of users in different treatment groups,

where $\mathbf{W}_{t3}$ is a weight matrix and $\mathbf{b}_{t3}$ is a bias vector. By combining the estimated ITE with the natural responses predicted by Eq.(6), we can obtain the responses of users in different treatment groups, and construct the supervised loss of this module with instances of different treatment groups in the training set,

Since in an online marketing scenario, the assignment of different treatments is usually not random, and this means that the collected training set usually has a significant distribution difference between the control and treatment groups. As shown in Figure 3, since only one type of response in each group is available for supervised training, differences in distribution between groups will exacerbate significant differences in estimated ITE between groups, such as $\tau^{\prime}_{k}$ and $\tau^{*}_{k}$. Therefore, ignoring this difference may increase the difficulty of ITE estimation and impair accuracy. To alleviate this problem, we propose a simple but effective intervention constraint module. The idea behind this module is to increase the difficulty of guessing the corresponding group from the ITE distribution of different groups, that is, to achieve a trade-off between the two through mutual interference. Previous studies have shown that similarities in ITE distribution across groups are beneficial for uplift modeling (Curth and van der Schaar, 2021b). Specifically, we use the embedding representation $\mathbf{e}^{xt}_{i}$, which is closely related to the uplift, to make predictions about which group this instance belongs to. We then train it with an inverse group label to generate perturbations as described above. This process can be expressed as,

Note that in the case of binary treatment, $\overline{t}_{i0}$ can directly take the opposite label. In the case of multi-valued treatment, a 0-1 mask vector needs to be generated from the original labels, and then the labels are negated.

After our EFIN training is complete, in the inference phase, we only need to use the treatment-aware interaction module to directly compute ITE, and then perform ranking and decision-making.

Following the settings of a previous work (Ke et al., 2021), we conduct experiments on two public datasets including CRITEO-UPLIFT (Diemert et al., 2021) and EC-LIFT (Ke et al., 2021). CRITEO-UPLIFT is a dataset open sourced by Criteo AI Labs for uplift modeling in a large-scale advertising scenario, which includes nearly 14 million instances, twelve continuous features, and binary treatments. EC-LIFT is a dataset of uplift modeling for different brands in a large-scale advertising scene, which is open sourced by Alimama. This dataset contains billions of instances, twenty-five discrete features and nine multi-valued features, and binary treatments. Due to the excessively large data scale, in order to facilitate training, we extracted about 40% of the instances from the original EC-LIFT dataset as the experimental dataset. The statistics of the two public datasets are shown in Table 1. We randomly split the two dataset for training and testing with a ratio 8/2. Note that since the modeling of user features and contextual features is consistent and does not require a special distinction, we use all the features in the above datasets in our experiments. Furthermore, following the setting of previous work, we treat treatment as a binary feature. To comprehensively evaluate our EFIN, we also include a product dataset collected from two weeks of online coupon marketing scenarios for credit card repayments. This product dataset uses a total of more than 200 features, involves 2 million users and has 2 million instances, 90% of which are used for the training set and the rest for the test set. In particular, instead of binary treatments in the public datasets, seven treatment options are included in product dataset.

We evaluate uplift ranking performance by four widely used metrics, i.e., uplift score at first $h$ percentile (LIFT@$h$), normalized area Under the uplift curve (AUUC), normalized area under the qini curve (QINI) and Weighted average uplift (WAU). We report the results with $h$ set to 30. We use a standard python package scikit-uplift¹¹1https://www.uplift-modeling.com/en/latest/ to compute these metrics.

To evaluate the effectiveness of our EFIN, we select a set of the most representative methods in neural network-based uplift modeling, including S-Learner (Künzel et al., 2019), T-Learner (Künzel et al., 2019), TarNet (Shalit et al., 2017), CFRNet (Shalit et al., 2017), DragonNet (Shi et al., 2019), GANITE (Yoon et al., 2018), CEVAE (Louizos et al., 2017), SNet (Curth and van der Schaar, 2021a), FlexTENet (Curth and van der Schaar, 2021b), EUEN (Ke et al., 2021) and DESCN (Zhong et al., 2022).

We implement all baselines and our EFIN in PyTorch 1.13²²2https://pytorch.org/. We use an AdamW optimizer³³3https://pytorch.org/docs/stable/generated/torch.optim.AdamW.html and set the maximum number of iterations to 20. To search for the best hyperparameters, we use QINI as a primary evaluation metric. We also adopt an early stopping mechanism with a patience of 5 to avoid overfitting to the training set. Furthermore, we use the hyper-parameter search library Optuna⁴⁴4https://optuna.org/ to accelerate the tuning process. The range of the values of the hyper-parameters are shown in Table 2.

The scenario is illustrated in Figure 4. Marketing in this scenario needs to launch different campaigns for different customer groups to motivate more users to pay the credit card bill within this platform. The treatments are promoted to some group of users once user tends to pay credit card bill on the platform. There are various types of coupons according to the constraints on bill amount in this scenario. Specifically, there are some small denomination coupons without a minimum amount requirement, and some higher denomination coupons requires minimum amount, thus the final number of treatments in this scenario is set as 7. The high-level architecture can be show in Figure 5. The user behaviors are pulled from data sources (some storage cluster) to generate features using Apache Spark⁵⁵5https://spark.apache.org/ and the candidate of treatments is coupons with various amount. The uplift model will score the uplift value for every user on each coupon. Finally, the promoter platform will further deliver coupons to user group with some resource constraints. Notice that our work focus on how to improve the performance of uplift model, which is the key component in the whole system.

To conduct online A/B experiment, we divide two sets of online traffic that do not affect each other, which involved hundreds of millions of users. The existing baseline on the online platform is a multi-head extended T-learner, where each estimator employs XGBoost (Chen and Guestrin, 2016) for computation. The baseline model and our EFIN are served for each independent online traffic for one month. As to evaluate the performance, we use two important online metrics: the marketing return on investment (ROI) and the number of monthly active users (MAU). Table 6 reports the relative improvements over the baseline. From the results in Table 6, we can find that our EFIN improves ROI and MAU by 10% and 8% compared to the baseline, respectively. This means that our EFIN can maintain a stable performance advantage over a period of time, and can indeed accurately capture the sensitive characteristics of different users to perform a reasonable treatment assignment.