Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing via Probability of Necessity and Sufficiency
Authors: Zexu Sun
Qiyu Han
Hao Yang
Anpeng Wu
Minqin Zhu
Dugang Liu
Chen Ma
Yunpeng Weng
Xing Tang
xiuqiang He
Venue: ICML 2025 spotlightposter (2025)
Keywords: Uplift modeling
Invariant learning
Incentives assignment
Online marketing
Primary area: applications
TL;DR: This paper proposes an invariant learning based uplift modeling method, which aims to solve the out-of-distribution problem in online marketing.

Abstract: In online platforms, incentives (\textit{e.g}., discounts, coupons) are used to boost user engagement and revenue. Uplift modeling methods are developed to estimate user responses from observational data, often incorporating distribution balancing to address selection bias. However, these methods are limited by in-distribution testing data, which mirrors the training data distribution. In reality, user features change continuously due to time, geography, and other factors, especially on complex online marketing platforms. Thus, effective uplift modeling method for out-of-distribution data is crucial. To address this, we propose a novel uplift modeling method \textbf{I}nvariant \textbf{D}eep \textbf{U}plift \textbf{M}odeling, namely \textbf{IDUM}, which uses invariant learning to enhance out-of-distribution generalization by identifying causal factors that remain consistent across domains. IDUM further refines these features into necessary and sufficient factors and employs a masking component to reduce computational costs by selecting the most informative invariant features. A balancing discrepancy component is also introduced to mitigate selection bias in observational data. We conduct extensive experiments on public and real-world datasets to demonstrate IDUM's effectiveness in both in-distribution and out-of-distribution scenarios in online marketing. Furthermore, we also provide theoretical analysis and related proofs to support our IDUM's generalizability.

Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing via Probability of Necessity and Sufficiency
Zexu Sun
Qiyu Han
Hao Yang'
Anpeng Wu Mingin Zhu Dugang Liu Chen Ma Yunpeng Weng 6
Xing Tang? 7 Xiuqiang He"
Abstract
1. Introduction
In online platforms, incentives (e.g., discounts, coupons) are used to boost user engagement and revenue. Uplift modeling methods are developed to estimate user responses from observational data, often incorporating distribution balancing address selection bias. However, these methods are limited by in-distribution testing data, which mirrors the training data distribution. In reality, user features change continuously due to time, ge- ography, and other factors, especially on complex online marketing platforms. Thus, effective up- lift modeling method for nut-of-distribution data is crucial. To address this, we propose novel uplift modeling method Invariant Deep Uplift Modeling, namely IDUM, which uses invariant learning to enhance out-of-distribution general- ization by identifying causal factors that remain consistent across domains. IDUM further refines these features into necessary and sufficient fac- tors and employs a masking component to reduce computational costs by selecting the most infor- mative invariant features. A balancing discrep- ancy component is also introduced to mitigate selection bias in observational data. We conduct extensive experiments on public and real-world datasets to demonstrate IDUM's effectiveness in both in-distribution and out-of-distribution sce- narios in online marketing. Furthermore, we also provide theoretical analysis and related proofs to support our IDUM's generalizability.
With the development of online platforms, online marketing has become increasingly important and competitive (Liu et al., 2023: Sun et al., 2024a). Assigning appropriate incen- tives to users has become a pivotal strategy for enhancing user conversion rates and boosting revenue. These incen- tives generally contain carefully designed contents (e.g., discounts, coupons). To achieve this purpose, uplift mod- eling has been proposed in recent years (Yao et al., 2021; Sun & Chen, 2024). For instance, Booking implements promotional strategies to enhance user satisfaction (Albert & Goldenberg, 2022), Meituan uses cash bonuses to stim- ulate user retention (Wang et al., 2023), Kuaishou utilizes virtual coins to increase users' playback duration (Ai et al., 2022). A primary challenge arises from the non-random assignment of incentives in observational data. For instance, platforms may assign incentives based on user age, indi- cating tendency to target younger users to enhance profit margins, which is called selection bias.
In recent years, with the development of uplift modeling, there have been many works proposed to solve the above challenge (Zhang et al., 2021). These works can be divided into three research lines: 1) Meta-learrer-buued. The ba- sic idea of this line is to estimate the users' responses by using existing predictive models as the base learner. Two of the most representative methods are S-Learner and T- Learner (Künzel et al., 2019), which adopt a global base learner and two base learners corresponding to the treat- ment and control groups, respectively. 2) Tree (or Forest)- based. The basic idea of this line is to employ hierarchical tree structure to systematically partition the user popula- tion into sub-populations that exhibit sensitivity to specific treatments. An essential step involves modeling the uplift directly by applying diverse splitting criteria, including con- siderations of distribution divergences (Radcliffe & Surry, 201 and expected responses (Zhao al., 2017; Saito et al., 2020). 3) Neural network-based. The basic idea of this line is to leverage the power of neural networks to develop estimators that are both intricate and versatile in predicting the user's 's response. CFRNet (Shalit et al., 2017) uses the Integer Probabilistic Metric (IPM) to solve the selection bias
GGaoling School of Artificial Intelligence. Renmin Univer- sity of China "School of Statisties, Renmin University of China Department of Computer Science and Technology, Zhejiang Uni- versity *College of Computer Science and Software Engineer- ing, Shenzhen University 'epaatment of Computer Science, City University of Hong Kong 'FTT, Tencent 'School of Big data and Internet, Shenzhen Technology University. Correspondence to: Xing Tang <xing.tang hotmail.com.> Xiuqiang He <hexi- uqiang @ sztu.edu.cn.>
Proceedings of the 42nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
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[4) Different kinds of short videos (ie., Fashion and Hobbies).
(b) Play counts of different user groups the same time scross different kinds short videos.
Play counts of group the different time across different short videos.
Figure I. The visualization of the out dittr--distrbuution problem in the online short video platform.
in the latent space. Dragonnet (Shi et al., 2019) constructs the target regularizer for modeling the prediction biases of the user response, which can reduce the estimation errors of the uplift.
mation over observational data, we introduce a balancing discrepancy part to balance the distributions between dif- ferent treatment groups. Moreover, we conduct extensive experiments on various datasets to evaluate the effectiveness of our IDUM model.
However, the main limitation of these methods is that they have only tested on data similar to the training data, which known as the in-distribution (ID) data. In real-world applications, user features suffer continuous changes due to varying time and different geographical environments. Thus, concerns arise regarding the performance of these methods when applied to users whose feature distributions differ from those of the training data (Zhou et al., 2022). As shown in Figure 1, this problem is more severe in short video online marketing scenario, where the features of the users are more complex than others. In Figure 1(b), we can see vast difference in the play counts between different user groups. The distribution of users' features may change over time, seasons, holidays, urban and rural areas, etc., resulting in the emergence of change in users' preferences, which also can be reflected in Figure 1(c). This can be regarded as (OOD) data generalization.
2. Related Work
Uplift Modeling, Recent years have witnessed significant attention in uplift modeling (Sun et al., 2024b; 2025), par- ticularly in the environment of online marketing (Zhang et al., 2021). This research predominantly focuses on model development and real-world applications. In cases of bi- nary outcomes, the standard approach entails constructing two classification models (Künzel et al., 2019), which in- volve separate conditional probability models for treated and control users. This two-model strategy, compatible with any conventional estimator such as regression trees (Loh, 2011), 1), is straightforward and versatile. However, it does not address the disparity in feature distributions between treatment and control groups. To overcome this, Künzel et al. (Künzel et al., 2019) introduced the X-Learner, which utilizes propensity scores (Caliendo & Kopeinig, 2008) to calculate weighted average of two estimators, thus miti- gating differences in feature distributions. For direct uplift modeling, a transformed response method (Athey & Im- bens, 2016) was proposed, yet its success heavily relies on the accuracy of propensity scores. Regarding continu- ous outcomes, the Causal Forest (Davis & Heller, 2017), a random forest-like algorithm, employs causal trees (Daron- deau & Degano, 1989) as its basic learner, offering a robust framework with theoretical support. With the emergence of deep learning in causal inference, many studies focus- ing on individual treatment effect (ITE) estimation have been introduced. TARNet (Shalit et al., 2017) features a two-head structure similar to the T-Learner, with a shared representation layer that facilitates the exchange of informa- tion between the heads. CFRNet employs distance metries (MMD and WASS) based TARNet's architecture to bal- ance the representation across both heads. To address the
the issue of out-of-distributie If we only use the previous methods on the specific data, we may get unreliable prediction results. Such unreliahility may lead to inappropriate incentive assignments, posing huge threat to users' experience. Therefore, an urgent demand is to develop uplift modeling methods that can effectively generalize to unseen testing data or different users.
In this paper, in order to solve the above challenges, we pro- pose a novel uplift modeling method Invariant Deep Uplift Modeling, namely IDUM. Specifically, our IDUM proposes an invariant property learning part aimed at enhancing out- of-distribution uplift generalization by identifying causal features with invariant properties across domains. By sep- arating these features into necessary and sufficient factors, we can learn the invariant features with finer granularity. Moreover, to reduce computational redundancy, we design a Huumbel-Sftmax--asee feature selection part to identify key subsets for invariant property learning. Additionally, to address the common selection bias issue of uplift esti-
2

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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
sample imbalance between treatment and control groups, Dragonnet (Shi et al., 2019) implements tri-head structure, incorporating a separate head for learning the propensity score. Different from the above methods, our IDUM focuses on the distributional shift of the testing data in the uplift modeling.
Framework (Rubin, 2005). Our aim is to predict the up- lift across multiple users. Generally, we consider the users used for training the model are sampled from the environ- ment e E E, the target users are sampled from environment e' E E. With an observed dataset De = {a 44 vf ) where N represents the number of samples. For each user i, as E xx denotes the features, i E {0, indicates the treatment assignment (1 for receiving an incentive, 0 otherwise), y y IR is the response variable. The target users are from a different environment e' E E and (#ff We where V represents the number of samples. This dataset only considers the feature shift without the corre- sponding treatment assignment or responses. Our goal is to learn a model from the dataset De to predict the uplift for the dataset D sampled from different environments e' E E. We treat this problem as the uplift prediction for Dut-of-Distribution users. The objective of uplift modeling is to evaluate the effect of treatment in on the response of for given user with features Ti, specifically calculating the difference between treatment and control responses as follows:
Invariant Learning. In recent years, invariant learning has become a critical field of research in machine learning, fo- cused on developing models that retain robust performance amidst distributional changes (Zhao et al., 2019). Many works on environmental generalization concentrate on iden- tifying invariances across training environments (Zhou et al., 2022). Recently, a strategy that has made sigmificant im- pacts involves learning features that enable a predictor to remain invariant across different environments (Creager et al., 2021; Lin et al., 2022; Hung & Chou, 2015), termed invariant learning in this paper. Such strategy is based on the theory of causality (Saengkyongam et al., 2023), where Structural Equation Models (Pearl, 2010) or causal graphs (Yao et al., 2021) are used to describe assumptions on the data generation process. The feature-conditooned label distribution invariance arises from the consistency of causal mechanisms across various environments. Recent theoreti- cal studies on invariant learning examine its failure cases in environment generalization tasks where environments are known prior (Chen et al., 2022). Invariant risk minimiza- tion (IRM) methodologies (Rosenfeld et al., 2020) present an approach for acquiring knowledge of invariant variables and functions. Based on this, some other works (Krueger et al., 2021; Lu et al., 2021; Ahuja et al., 2021) further extend the IRM framework involves the incorporation of elements from game theory, variance penalization, informa- tion theory, as well as the integration of nonlinear prediction functions. Additionally, recent studies have applied the IRM framework to large neural networks, thereby contribut- ing to its advancement (Rosenfeld et al., 2020; Guirajani & Lopez-Paz, 2020). Based on the probability of neces- sity and sufficiency (PNS), some works design structures to discover the PNS features. CaSN employs probability of necessity and sufficiency (PNS) to extract enviromment- invariant information (Yang et al., 2024). Diverging from the aforementioned approaches, our IDUM focuses on the probability of necessity and sufficiency within generalized uplift modeling methods. Moreover, taking into account computational costs, we design additional structures to ad- dress this concern.
7f =f of (0),
(1)
In the real world, we can only observe one of the two re- sponses for each user, that is, either yf (1) or vf( is the accessible factual response, the other is the counterfactual one remained unavailable.
For simplicity, subscript and superseript e will be omit- ted where the context remains clear. Although the uplift or individual treatment effect in Eq. (1) cannot be directly iden- tified due to the unobserved counterfactual, the conditional average treatment effect (CATE) offers a viable estimator for uplift under common assumptions (Shalit et al., 2017, 7: Abrevaya et al., 2015). The CATE for a sub sub-population or individual is defined as:
T(x) = E (Y X 2) EY((0) X = x)
E(Y T =, X = x) B(Y T 0, X x)
(2)
After that, we can derive the uplift r(x) by only leveraging the observational dataset.
3.2. Probability of Necessity and Sufficiency
Invariant learning is widely employed for out-of-distibbttin generalization (Arjovsky et al., 2019; Liu et al., 2021). The fundamental assumption of invariant learning posits that, given the features X, response Y and treatment T, only the environment invariant features X can reliably predict the response, while other environment-specffee features X" are spurious correlates of the response, thereby compromising the model's 's generalizability. Hence, invariant learning aims to identify domain- invariant features that satisfy the distri- butions of responses Pa ( .T) = ( (Y)x, (x,T) across environments e and e'.
3. Preliminaries
3.1. Problem Setup
Following previous studies (Sun et al., 2023b; Zhu et al., 2023; He et al., 2024), we address the problem of uplift modeling within the framework of the Potential Outcome
3

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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
To further analyze the invariant features, Probability of Ne- cessity and Sufficieney (PNS) (Pearl, 2022) is proposed to describe the probability that event A occurs if and only if event B occurs, which separates the invariant features into necessary and sufficient features. This probability operates two events to compute the probability that event is nec- essary and sufficient cause for event B. To better understand this, have the following definitions:
Optmizztion Objactive
ho
disc (1% 1%)
Treatment Response
Control Response
Balancing Discrepency
Invariant Property Learning
Definition 3.1 (Probability of necessity, PN).
Suffecient Term S.F. (h, e)
Mask
PNS Upper Bound
PN P(x A)
Necessary Term
PN the probability that, given that events A and B both occur initially, event B does not occur (e.g., B) after event A is changed from occurring to not occurring (e.g.. A).
Rey (h, @, v)
m(a=")
NC.
Definition 3.2 (Probability of sufficiency, PS).
PS = P (BA A, B):
(4)
Representation Network
PS is the probability that, given that events A and B both did not occur initially, event B occurs after event is changed from not occurring to occurring.
Definition 3.3 (Probability of necessity and sufficiency, PNS).
C
PNS PN. P)A B),
(5)
Figure 2. The whole structure of our IDUM, where ho and hı are the prediction heads of treatment and control groups. For simplic- ity, we use h to represent the response prediction in Section 4.
PNS is the sum PN and PS, each multiplied by the prob- ability of its corresponding condition. PNS measures the probability that event A is necessary and sufficient cause for event B.
the causal and invariant features to remove such spurious relationships. Technically, inspired by Pearl (2022); Yang et (2024), we design an invariant property learning part for enhancing the out-of-distribttion uplift generalization. In detail, propose the theories and the objective for extracting sufficient and necessary features based on PNS in the uplift generalization.
4. Methodology
this section, we propose the IDUM model, a novel method to improve the out-of-distribution generalization for uplift modeling task. To begin with, we design invariant prop- erty learning part to learn the sufficient and necessary fea- tures, capturing the invariant pattern behind data simulta- neously. To reduce the computational cost, we employ a feature selection part with a neural network-basee masking function. Finally, we introduce a balancing discrepancy part to address the selection bias issue in the incentive assign- ment process. The whole structure of our IDUM is shown in Figure 2. The notations used in this paper are presented in Appendix A.
PNS Risk and Upper Bound. We begin by introducing the basic backbone (ax), which is constructed by multi- layer perceptron (MLP) on the features of the treated and control samples. Based on the conceptions of sufficient and necessary features, we have the definition of PNS risk to learn the PNS value.
Definition 4.1 (PNS Risk). The PNS Risk defined over the distribution of target environment e' E
4.1. Invariant Property Learning
Re (h, O V) E Ege (x-))))) [lia"", * vl
As mentioned in Section 1, existing uplift modeling methods are hard to handle the distribution shift, therefore perform poorly in the out-of-distribution testing data. As proved in Zhou et al. (2021), the distribution shift issue is probably caused by the spurious correlation between the user features and the response. Therefore, an intuitive solution learn
(h,())
Ege p PX()) [h( =-
(h,,)
(6)
where SF, θ) and NC. T denote the sufficient

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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
and necessary terms, respectively. æf and xF are the special implementations of X", where x² * Ø.. e and vi are the parameters for learning the sufficient and necessary terms.
We present the proof in Appendix B. The upper bound for the PNS risk in Eq. (8) comprises two components: (1) the sufficiency evaluator SFerr (h, θ) and (2) the monotonicity measurement MD (+, V). In this upper bound, the neces- sary term NC. (h, v) is assimilated into the Monotonic- ity measurement M (O, V). The minimization process of Eq. (6) with respect to its upper bound, Eq. (8), entails ensuring the satisfaction of Monotonicity.
Variable X has a high probability of being the sufficient and necessary feature of Y when the PNS value is small. However, computing the probability is a challenging prob- lem for gathering counterfactual data (i.., xx and );), which may be impractical or unattainable in real-world sys- tems. Fortunately, the PNS defined on the counterfactual distribution can be directly estimated from the data under appropriate conditions (i.e., Exogeneity and Monotonicity). Definition 4.2 (Exogeneity (Pearl, 2022)). X is exogenous relative to variable Y w.r.t. source and target environments e and e', if the probability is identified by conditional proba- bility Pe (Ydo(x===*) y x T) PY = y X
OOD Generalization. In uut-of-distributtio (OOD) uplift generalization, only source data gathered from environment are available, whereas the target environment e' remains inaccessible throughout the optimization procedure. Con- sequently, directly assessing the risk on the target environ- ment, denoted as (h, θ V), is unfeasible. Hence, we establish the linkage between the risks associated with the source environment, R. (h, O V), and the target environ- ment, Re (h, θ V).
x: 7) and Pe. (Vdo(x-=<)) = y X T) = (Y = y
X ==, , .))
We introduce the divergence measurement known as B di- vergence (Ganin et al., 2016) and apply variational approxi- mation to weight the term R (h, θ v). Formally, 3 diver- gence quantifies the dissimilarity between environments e and e', as formally defined below.
Definition 4.3 (Monotonicity (Pearl, 2022)). Y
is monotonic relative to X if and only if either
P (Ydo(X===") y, Ydo(X"==") Fy x T) = 0
or P (Ydo(x==>>) fu y, do((x====)) y xx (T =0
The definition of Exogeneity delineates that the disparity be- tween the counterfactual data and conditional distributions diminishes when X is exogenous with respect to Y, while Monotonicity illustrates the monotonic effect of variable X on Y. Then, the identifiability of PNS can be described as the following lemma.
Ba(e'lle) = (a.tt.))~ (c(z,t.)))
(9)
Based on (e'e'll), we connect the risks on the source and target environments by Theorem 4.6.
Lemma 4.4. (Pearl, 2022) If X is exogenous relative to Y, and Y is monotonic relative to X then
Theorem 4.6. The risk in the target environment is bounded by the risk in the source environment:
PNS( = Pe. (Y X = =x=,, =x,T) TT)
(h, v) < lim
g B [e) (O,))"
(7)
- PY = X = T),T).
+2[SF (h. 2)) + Ee,
According to Lemma 4.4, the computation of PNS becomes feasible through observational data under the assumptions of Exogeneity and Monotonicity. This enables the quantifi- cation of PNS even in the absence of counterfactual data. The proof of Lemma 4.4 is provided by Pearl (2009), and its applicability to our problem setting can be directly extended. Subsequently, we seamlessly incorporate the measure of Monotonicity into the PNS risk by deriving an upper bound.
where Ee (X, == (x x & supp(e)) sup(Rerreeh, 0, v))
We provide the proof in Appendix B. Here supp(e) is the support set of source environment distribution Pa PX)
R O v) (xxxaa) [SF (h, ()
+h, V)).
Proposition 4.5 (Upper Bound of PNS Risk). Given the target environment, let the Monotonicity measurement be:
Theorem 4.6 establishes a connection between the risks of the source and target environments. Within Theorem 4.6, (X, T, Y) delineates the expectation of the worst risk in unknown area, where the data sample (æ, f, t) does not belong to the support set supp(e) of the source environment. When the observations X in e and e' share the same support TX, tends towards 0.
( v-- = E ((.. E P9 ((x)) Ex PPX
11 11( t) # h((",,)) f),,
Then, we can gel:
Re Re, θ v) MM, W) (t,, V)
set, the term
< (M 4) 9).
In many real-world uplift modeling scenarios where the distribution e is not directly accessible, we examine the
(8)
5

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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
association between the expected risk based on the source environment distribution and the empirical risk computed from the data of the source environment. Similarly, we can assess the empirical risks with respect to SFe (h, @) and (h, V). Subsequently, we leverage PAC-learning (De- nis, 1998) to formulate theorem in the following, establish- ing an upper bound for the discrepancy between empirical risk and expected risk.
where k: [x+H] E 2., is the number of features expected to be obtained, H is the number of input features. Specifi- cally, in Eq. (10), let ity vector. For any feature dimension j E 1..... H, it holds that 2j 2 O and Σ; 2j = 1. With a predefined temperature C >> O, the computation of each feature dimension in the mask vector can be expressed below (Lv et al., 2022).
w(x²) E IR represent a probabil-
exp ((log 23 + n1)) /9)
Theorem 4.7. Given parameters O Mr for any h, prior distribution Xx= 9 and X )x which make B.n KL, (P (( (x))) and
m, = max LE(1 (E()....))
-Ø'=1 exp (log zy + 1 /5)
(11)
where E {1...., k} denotes the index of the selected feature, viş = = Log log u/), and u/. ~ Uniform(O, 1) denotes uniformly distributed sampling. Finally, we can get the masked features xm by multiplying the original features af with the resulting mask vector m(x))
Eg KL ( o (XX)= = {xx))] (xx) both lower than a positive constant C, then with a probability at least 1 - over source environment data,
(1) SFa(h, Q)- - -h, 0) is upper bounded by
s x m(x²),
(12)
In(n/c) +C, 2(n 1)
KT.
KT. p0 (x क (X) = (())))
where @ denotes the element-wise multiplication. Remark- ably, the same procedure is applied to T.
where n is the number of the source data.
4.3. Balancing Discrepancy
(2) (0, (O, v is upper bounded by
Up to now, we have adopted invariant learning to enhance -uttof-distribution uplift generalization. However, there re- mains the issue of selection bias, which is common when estimating uplift on observational datasets. To address this, we apply the distribution discrepancy regularizer from CFR- Net (Shalit et al., 2017), which achieves a balanced represen- tation by minimizing the distributional differences between treatment and control groups. A typical metric used for measuring the distribution discrepancy is the Integral Prob- ability Metric (IPM) (Müller, 1997; Sriperumbudur et al., 2012), which is formally defined as.
Ee KL (Po xx()) (x))))l
In(refe) 2(m - 1)
+ BL (x' Φ ((X)= = +())))+x=++
+
+ 2C.
The proof is provided in Appendix B. Theorem 4.7 illus- trates that as the sample size increases and the terms involv- ing KL divergence diminish, the empirical risk computed on the source environment dataset converges towards the expected risk. By combining Theorems 4.6 and 4.7, we can get the expected PNS risk on the target distribution by leveraging the empirical risk computed on the source data.
disc (Pg, PS) supho.h.eRk Pn- [hs (z. t)] Ba- (o 8)]
(13)
where PS = ( (+))) and Pg 1 (a)) denote the feature distributions of the treatment and control groups in the representation space, respectively. ho t) and hi (z, t) represent the prediction heads, which are optimized by the cross entropy loss. For ease of understanding, we use h( 4) to represent them in the following description. For function families H with sufficient richness, when the discrepancy between the distributions Pt and Pt equals zero, it follows that P Pg holds (Shalit et al., 2017). Consequently, minimizing this discrepancy entails aligning the means in the feature space.
4.2. Feature Selection
After we have designed the above PNS risk upper bound, problem that needs to be solved is that the dimension of the shared feature representation ((x) in the uplift model is always large, thus, the computational cost to find x" is big. To address this challenge, we employ a neural network- based masking function, denoted as w.), which determines the contribution of each feature in the uplift estimation. Ad- ditionally, we utilize the Gumbel-Softmax trick (Jang et al., 2016) to constrain the model, enabling the acquisition of approximate h-hot mask vector m (..).. The w-ratio features with the greatest contribution are identified as the desired key features, while the remaining features are deemed irrele- vant or redundant. The formulation of (x=) is as follows:
4.4. Optimization and Training Procedure
From above description, we know that the learning process of 1o (X" ((X) = ((x)), coupled with the feature selection outlined in Section 4.2, can solve the uplift gen- eralization problem. Throughout the learning phase, our
m(a*)= = Gumbel- Gumbel-SSftmax(((p (ú (x)) kH) E H (10)
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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
Table 1. Overall comparison between our IDUM and the baselines on ID Lazada and Production datasets. We report the results over five
random seeds. The best results and second best results are bold and underlined. respectively.
Lazada Dataset (ID)
Production Dalaset(ID)
Method
AUUC
QINI
KENDALL
AUUC
QINI
KENDALL
S-Learner
0.0117 + 0.0029
0.3826 + 0.0377
0.1073 = 0.0141
0,2450 + 0.0232
0.3292 : 0.0258
0.1643 0.0169
T-Learner
0.0125 + 0.0027
0,4442 : 0.0245
0.1197 = 0.0140
0.2461 + 0.0229
0.3486 : 0.0247
0.1671 + 0.0161
TARNet
0.0171 = 0.0026
0,4457 = 0.0217
0.1372 = 0.0121
0.2493 + 0.0218
0.3428 + 0.0227
0.1698 + 0.0173
CFRNet-mmmd
0.0271 = 0.0036
: 0.4610 0.0219
0.1698 = 0.0132
0.2691 + 0.0224
0.3408 = 0.0246
0.1915 0.0139
CFRNet-wass
0.0273 = 0.0034
0.4465 # 0.0209
0.1753 = 0.0137
0.2579 = 0.0223
0,3503 = 0.0246
0.1921 + 0.0147
DragonNet
0.0241 = 0.0037
0.4392 + 0.0292
0.1444 = 0.0132
0.2527 + 0.0201
0.3476 + 0.0230
0.1747 + 0.0173
EUEN
0.0267 = 0.0033
0.4456 + 0.0237
0.1523 = 0.0113
0,2793 + 0.0209
0.3693 = 0.0234
0.2004 0.0193
UniTE
0.0189 = 0.0030
0.4563 = 0.0283
0.1457 = 0.0144
0.2408 + 0.0211
0.3681 = 0.0225
0.1997 + 0.0167
TEED
0.0120 + 0.0026
0.4395 + 0.0234
0.1256 = 0.0129
0.2492 + 0.0239
0.3515 + 0.0241
0.1695 0.0167
IDUM
0.0270 + 0.0023
0.4646 + 0.0184
0.1798 = 0.0137
0.2907 + 0.0248
0.3700 + 0.0255
0.2091 + 0.0154
objective is to minimize the risk under the worst-case sce- nario induced by XT,. namely, the maximum PNS risk resulting from the selection of pa (X m (xx) ((x)).
the Alibaba Group. In the actual production setting, treat- ment assignment is selective owing to operational targeting strategies. Our training dataset comprises data characterized by significant treatment bias collected under these condi- tions. Additionally, we have a slightly smaller subset of users unaffected by the targeting strategies, where treatment assignment follows randomized controlled trials (RCT) for -uttr--distribution (OOD) testing.
Minimizing the upper bounds established in Theorem 4.6
and 4.7 can be simulated through the following optimization procedure:
min max.Ma.m (G, V) + SF (h, (h,,,, m,,)) +) O.h.m, V
+ disc (P' P8) + ALKL.
(14)
Production dataset. This dataset comes from an industrial production environment, specifically one of the largest short- video platforms in China. Clarity serves as a crucial user experience metric for such platforms. A decrease in clar- ity can significantly impact user satisfaction on the plat- form. Hence, we conducted random experiments over the course of week, wherein high-clarity videos (t 1) were provided to the treatment group, while low-clarity videos (t = 0) were provided to the control group. We collected the total play counts of users' short videos over the week and quantified the impact of resolution degradation on user ex- perience. To enhance data robustness and mitigate response variance, we discretized each user's response (i.e., total play counts) into four levels. Furthermore, for each user group, we collect data at two distinct time points to facilitate out-of- distribution (OOD) testing. Moreover, the dataset statistics and visualization are presented in Appendix A.
subject to
-لا hz 1|2 > 8,
& (Xx) (xxx)()))))) (xx=)) where LKL= EL pp (x
+ KL (
X m Φ (X) (x)) [T= )) ha t)
is the prediction head of the response variable, and the optimization function can be the cross entropy loss. The constraint ||=r 11,112 > is established to ensure d- S-mmanttic Separability (Yang et al., 2024). This criterion stipulates that the semantic meaning should be discernible between o and , when their distance exceeds certain threshold. The absence of this constraint may result in nearly identical values representing vastly different semantic information, leading to inherently unstable and chaotic data. Consequently, the final optimization objective derived as follows:
LIDUM= = min max M/.. (0, V) + SF m, +) @.h.m, &
Baselines and Metrics In this paper, we compare our method with the commonly used uplift modeling methods, S-Learner (Künzel et al., 2019), T-Learner (Künzel et al., 2019), TARNet (Shalit al., 2017), CFRNet (Shalit et al.,
+ disc (Pb, Pb) + + || - 1 + ALKL-
(15)
2017), DragonNet (Shi et al., 2019), EUEN (Ke et al.,
5. Experiments
2021), UniTE (Liu & Hou, 2023) and TEED (Sun et al.,
2023a). Following the previous works (Sun et al., 2023b;
5.1. Experimental Setups
2024c), we evaluate the performance of the methods by
AUUC, QINI and KENDALL. More details are presented in Appendix A.
Datasets.
Lazada dataset (Zhong et al., 2022). We uti- lize a large-scale production dataset obtained from real voucher distribution operations at Lazada, a prominent e- commerce platform in Southeast Asia (SEA) operated by
Implementation Details We implement all baselines and our IDUM based on Pytorch 1.10, with Adam as the opti-
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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
Table 2. Overall comparison between our IDUM and the baselines on OOD Lazada and Production datascts. We report the results over
five random seeds. The best results and second best results are bold and underlined. respectively.
Lazada Datasel (OOD)
Production Dataset (OOD)
Method
AUUC
QINI
KENDALL
AUUC
QINI
KENDALL
S-Learner
0.0093 = 0.0028
0.3581 + 0.0393
0.1036 0.0137
0.2444 + 0.0229
0.3284 : 0.0263
0.1632 0.0172
T-Learner
0.0101 = 0.0027
0,4392 + 0.0228
0.1032 = 0.0124
0.2442 + 0.0235
0,3411 = 0.0244
0.1617 + 0.0159
TARNet
0.0104 = 0.0025
0.4448 = 0.0204
0.1081 = 0.0118
0.2365 + 0.0205
0.3347 = 0.0231
0.1684 + 0.0161
CFRNNet-mmd
0.0262 = 0.0037
0.4618 + 0.0210
0.1737 = 0.0126
0.2665 + 0.0214
0.3383 = 0.0228
0.1894 0.0143
CFRNet-wass
0.0269 = 0.0036
0.4332 = 0.0219
0.1742 = 0.0137
0.2583 + 0.0206
0.3391 = 0.0237
0,1912 + 0.0157
DragonNet
0.0224 + 0.0035
0.4179 + 0.0279
0.1040 = 0.0124
0.2423 + 0.0214
0.3287 = 0.0212
0.1724 + 0.0169
EUEN
0.0250 = 0.0032
0.4270 + 0.0225
0.1428 = 0.0107
0.2755 + 0.0210
0.3632 = 0.0220
0.1995 0.0180
UniTE
0.0122 = 0.0028
0.4499 = 0.0291
0.1284 = 0.0131
0.2298 + 0.0221
0,3568 = 0.0215
0,1899 + 0.0154
TEED
0.0102 + 0.0031
0.4239 + 0.0268
0.1089 0.0128
0.2237 + 0.0297
0.3275 + 0.0223
0.1682 + 0.0153
IDUM
0.0274 + 0.0026
0.4633 + 0.0191
0.1790 = 0.0152
0,2847 + 0.0265
0.3681 + 0.0245
0.2051 + 0.0166
mizer and maximum iteration count of 50. We use the QINI as a reference to search for the best paper-parameterss for all baselines and our model. We also adopt an early stop- ping mechanism with a patience of 5 to avoid over-fitting to the training set. Furthermore, we utilize the hyper-parameter search library Optuna (Akiba et al., 2019) to accelerate the tuning process, all experiments are implemented on NVIDIA A40 and Intel(R) Xeon(R) 5318Y Gold CPU @ 2. 10...Zz.
Therefore, our proposed IDUM can be considered as an effective generalized uplift model in online marketing.
5.3. Ablation Study
In this section, we conduct ablation studies on the OOD testing data to assess the necessity of each component in our proposed IDUM model. Specifically, we sequentially re- move the Integral Probability Metrics-based representation Balancing Discrepancy component (BD), the Invariant Prop- erty Learning with PNS risk (IPL), and the Feature Selection with Gumbel--Sotmax of IPL. (IPL-FS). We then tailor three variants of IDUM, namely w/o BD, w/o IPL, and w/o IPL- FS. From the results reported in Table 3, it is evident that removing any part of IDUM leads to performance degra- dation. Firstly, the IPM regularization for representation balancing helps address the internal selection bias between the treatment group and the control group. Secondly, the IPL. part, serving as a crucial component for managing the distribution shift between training and testing data, signif- icantly contributes to the accurate estimation of uplift, as evidenced by the substantial performance drop when it is removed from IDUM. Lastly, the adversarial feature selec- tion part aids in efficiently learning the invariant property hidden in the data, thereby further enhancing the robustness of our IDUM model in out-of-distribution scenarios.
5.2. Overall Performance
To evaluate the performance of our IDUM on both in- distribution (ID) and out-of-distribution (OOD) testing data, we conduct several experiments on the Lazada dataset and the Production dataset. The results are reported in Table and 2, where we can observe: 1) Among all the baseline methods, the S-learner, T-laaner, and TARNet exhibit the poorest performance across both ID and OOD) experiments. We speculate that their simplistic model architectures, lack- ing further constraints, struggle to mitigate both the selec- tion bias and the distribution shift between training and testing sets, consequently leading to inaccurate uplift predic- tion in real-time marketing scenarios. 2) CFRNet-wass, and CFR-mmd consistently demonstrate superior performance compared to other baselines. This can be attributed to their utilization of Integral Probability Metrics, such as Maxi- mum Mean Discrepancy and Wasserstein distance, which facilitate the mitigation of selection bias between treatment and control groups. However, they still exhibit challenges in coping with the distribution shift problem, as evidenced by their comparatively lower performance in OOD experiments. 3) Encouragingly, our IDUM consistently outperforms all baselines across both the Lazada dataset and the Production dataset, particularly on OOD testing data. This demon- strates the effectiveness of the carefully designed invariant property learning part within IDUM, which encompasses the PNS risk and adversarial feature selection components, in robustifying the uplift model in collaborative manner.
5.4. Sensitivity Analysis
In this section, we conduct nut-of-distribuu (OOD) ex- periments to analyze the sensitivity of each important hy- perparameter in our framework. Specifically, we vary the weight of IPM with a E {0.001, 0.005, 0.01, 0.05, 0.1), the weight of the semantic constraint with 3 E (0.001, 0.005, 0.01, 0.05, 0.1), the weight of KL diver- gence with X E {0.01, 0.05, 0.1, 0.3, and the value of temperature with Ç {0.5, 1, 1.5, 1,5, 2.5). The results are presented in Figure 3. It is evident that extreme val- ues of a for representation balancing regularization may adversely affect the model performance. Regarding the se-
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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
Table Ablation study of our IDUM. We report the results over five random seeds. The hest results and second best results are hold and
underlined. respectively.
Production Dataset (ID)
Production Datasel (OOD)
Method
AUUC
QINI
KENDALL
AUUC
QINI
KENDALL
IDMM
0.2907
0.0248
0.3700 + 0.0255
0.2091 0.0154
0.2847 0.0265
0.3681 + 0.0245
0.2051
0.0166
w/o BD
0.2863 + 0.0246
0.3658 + 0.0217
0.2041
0.0277
0.2710 + 0.0227
0.3383 + 0.0264
0.1801
0.0153
W/O IPL
0.2680 + 0.0206
0.3531 + 0.0236
0.1939 + 0.0162
0.2732 + 0.0235
0.3475 + 0.0204
0.1781 = 0.0173
w/o IPL-FS
0.2891 + 0.0224
0.3651 + 0.0214
0.2087 + 0.0159
0.2737 + 0.0251
0.3242 + 0.0253
0.2039 = 0.0124
0.49
ASMIC
0.40
AMSC
0.40
AUXC
0.48
AUUC
QINI
ONNI
OINI
0.25
0.90
0.30
00.00
0.30
0.25
0.21
0.20
0.29
0.35
0.15
0.002
0.805
0.05
0.1
0.092
0.01
0.05
0.5
2.5
less wrightt
eerigine
less seriget
less areggge
(a) Weight of IPM.
(b) Weight of constraint.
(c) Weight of KL. divergence.
(d) Value of softmax temperature.
Figure 3. Sensitivity analysis our IDUM on the OOD Production dataset. We report the results over five random seeds.
mantic constraint, the best uplift estimation performances are consistently achieved with a moderate value of B. Addi- tionally, our IDUM model demonstrates varying tendencies across these three metrics when the value of À for KL diver- gence in invariant property learning is adjusted, indicating the need for careful tuning in real-world scenarios. Lastly, the IDUM model exhibits robustness fluctuations in the softmax temperature S, consistently selecting crucial fea- tures effectively.
Impact Statement
The proposed IDUM to enhance uplift modeling for incen- tive allocation in online marketing by addressing distribution shifts and selection bias, which holds significant societal implications. Ethically, IDUM's s ability to generalize across diverse user populations could promote fairer incentive dis- tribution by reducing biases tied to spurious correlations (e.g., age or geography). This aligns with ethical AI princi- ples by ensuring equitable access to promotional benefits, However, reliance user data necessitates stringent pri- vacy safeguards to prevent misuse of sensitive information. Future deployment should incorporate transparency mecha- nisms to audit algorithmic decisions and mitigate unintended discrimination.
6. Conclusion
In this paper, we propose a novel method called Invariant Deep Uplift Modeling, namely IDUM, construct gen- eralized uplift model for incentive assignment in online marketing, Our proposed IDUM incorporates three key components to enhance -fiitr-iittttiionn uplift generaliza- tion. Firstly, an invariant property learning part is designed to identify necessary and sufficient features with domain- invariant characteristics. Secondly, to optimize computa- tional efficiency, we implement a Gummbel-Softmax-basss feature selection mechanism that identifies crucial feature subsets for invariant learning. Thirdly, balancing dis- crepancy component is introduced to mitigate distributional differences across treatment groups Through extensive empirical evaluations and thcoretical analysis, we demon- strate the effectiveness of our IDUM and provide rigorous generalization guarantees for it.
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Table 4. Statisties of the public datasct Lazada and real-world dataset Production.
Training Data
Testing Data (ID)
Testing Data (OOD)
Dataset
Features
Treated
Control
Total
Treated
Control
Total
Treated
Control
Total
Lazada
83
0.64 M
2.27 M
4.17 M
0.28M
0.32M
0.60M
0.47M
0.43 M
0.91 M
Production
104
1.91M
4.22M
6.13M
0.56M
0.61M
1.17M
0.37M
0.40M
0.77M
==
t=
Figure 4. The visualization of the Production dataset. As f increases, the clarity of the video correspondingly enhances.
A. Additional Experiments
A.1. Dataset statisties
In this section, we provide the statistics of the datasets that we used in our work, where the selection bias and out-of- distribution issues exist. The statisties of those two datasets are summarized Table Moreover, the visualization the Production dataset is provided Figure 4.
A.2. Baselines and Metries
present a detailed description of the baselines we used in the following:
S-Learner (Künzel et al., 2019): S-Learnr is a kind of meta-leamee method that uses single estimator to estimate the response without giving the treatment a particular role.
T-Learner (Künzel al., 2019): T-Learer is similar S-Learner, which two estimators for the treatment and control groups, respectively.
TARNet (Shalit et al., 2017): TARNet is a commonly used neural network-basee uplift model. uses the shared bottom network to extract feature information.
CFRNet (Shalit et al., 2017): CFRNet (i.e., CFRNet-wass, CFRNet-mmd) applies an additional loss to TARNet, which forces the learned treated and control feature distributions to be closer.
DragonNet (Shi et al., 2019): DragonNet exploits the sufficiency of the propensity score for estimation adjustment and regularization procedure based the non-parametric estimation theory.
EUEN (Ke et al., 2021): EUEN is an explicit uplift modeling approach, which can correct the exposure bias.
UniTE (Liu & Hou, 2023): UniTE adopts the Robinson Decomposition (Bratteli & Robinson, 2012) framework, and design MMoE (Ma et al., 2018) based structure for uplift prediction.
TEED (Sun et al., 2023a): TEED is novel direct learning framework along with distribution adaptation and reliable scoring modules, which can solve the treatment effect estimation problem across environments.
13

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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
Table Notation Table of the notations in this work.
Notation
Definition
and e
Two different environments
X
User features
X
Environment invariant features
X
Environment specific features
Y
Response
T
Incentive
(-))
The basic backbone of feature encoder Intervention operation
do(.)
h())
Response prediction head Sufficient term
SF(.)
NC(.))
Necessary term
Parameters of the sufficient term Parameters of the necessary
V
Bg (II-)
3 divergence between environments Prior distribution of X
xx
The worst risk in unknown area Monotonicity measurement
E
Expectation
ml-)
Mask vector
KL(-1)
KL divergence
Element-wise multiplication
We present the detailed description of the metrics we used in the following:
AUUC (AREA UNDER UPLIFT CURVE): A common metric to evaluate the area under the uplift curve (Rzepakowski & Jaroszewicz, 2010), We use the CausalML package (Chen et al., 2020) to implement the metric.
QINI (QINT COFFFICIENT) (Mouloud al., 2020): A common metric evaluate the under the qini curve, different from AUUC, it scale the responses in control group.
KENDALL (KENDALL'S ' RANK CORRELATION) (Mouloud al., 2020): metric to evaluate the average predicted uplift and the predicted uplift in each bin, we report the result of 20 bins.
And for the reading clarity, we provide a notation table in the following.
A.3. Computational Complexity
In this section, we show the computational complexity in the following.
For the invariant property learning module, the computational complexity of the objective loss and negative log-likelihood linear, denoted as O(n). The complexity the KL divergence, however, O(n d), where d represents the feature dimensionality. For the feature selection module, the computational complexity of the linear transformation and batch normalization in forward propagation is O(n x h). where is the input dimensionality and h is the dimension of the hidden layer. In the mask generation phase, the Gumbel-Softmax operation is applied iteratively À times, resulting in complexity of O(k x m), where m is the number of mask elements. Consequently, the overall complexity of the mask generator can be expressed as Onn x h + & x m). For the discrepancy balancing module, for the computational complexity of IPM, MMD distance is employed, the complexity increases to On²)). ). In summary, the overall time complexity of the algorithm Onn²) + O(n h) Ol x m).
14

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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
Train treatment group
Train treatment group
Test
Test
(a) Lazada Dataset
(b) Production Dataset
Figure 5. Visualization of dataset distribution for in-distribution and out-of-distriuttio..
A.4. Analytical Experiments
To better help readers understand our motivation, i.e., the necessity addressing selection bias and OOD problems in a unified way. we visualize the distribution of the training set (including treatment and control groups) and the test set of the dataset used in the experiment. This is shown in Figure 5, which illustrates the distribution gaps found by our model. Combining the results in Tables I and 2, we see that this property makes our model more generalizable than existing baselines under different test settings.
A.5. Online Experiment
To further show the effectiveness of IDUM, we conduct an online experiment evaluate our IDUM against the baseline CFRNet, and we keep it for three days.
The experimental setups are listed in the following:
In-Distribution (ID) Test: We selected two user groups with similar distributions to the training data.
Out-of-Distribution (OOD) Test: We used two user groups with distinct distributions to assess generalization.
Due to the constraints of online inference, we could not obtain the true responses for users unaffected by the deployed algorithm. Instead, compared the watch time improvement and the cost reduction across experimental groups the key metrics.
Table Online experimental results.
(a) Watch Time Improvement (%)
(b) Cost Reduction (%)
Method
ID
OOD
Method
ID
OOD
CFRNet
0
0
CFRNet
0
0
IDUM
0.012%
0.028%
IDUM
-1.21%
-1.75%
We report the percentage of watch time improvement relative to CFRNet's performance (baseline, set at 0). And also, we evaluate the cost of two methods, for that we assign less incentives (-1.21% and -1.75%) to the user group and get competitive performance (0.012% 1022 and 0.028%).
15

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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
B. Proofs
B.1. Proof Proposition 4.5
To explicitly define the Monotonicity evaluator, we decompose the original objective into three terms: the sufficiency
objective SF )), the necessity objective NC (h, V), and the Monotonicity evaluator objective M (O, V) The Monotonicity term MD (O, V) can be further decomposed follows:
M (e, v) SF (1, (h, V)) + (1 (h, NC. V).
(16)
We can further derive Eq. (16) as follows.
M (0, v = (F, - + (1- (1. 0) (C.(h.
SF (N. V) - 2h, 9)NC. (h,
(17)
(h, O v) 25F (C,
Then we can rewrite the original objective Eq. (6) by
Rh, 6, V) (e, v) + (h, O)NC. V).
B.2. Proof Theorem 4.6
The rationale behind Theorem 4.6 to establish a connection between the risk observed in the source environment and that in the target environment. To prove the result stated Theorem 4.6, we make reference to the technical details presented in (Germain al. 2016). We initially define u (= , t, 3) & sup(e)), allowing us compute the value of 5-Monotonicity measurement samples originating from the target environment but not encompassed within the source environment:
(aa.v)~ (ax
E (x [ (xr", () h(**,()) ()]
= -
( ((x))((m))
[M( ,I) # M(x", D)] = =MM (O, V
Likewise, the aggregate risk associated with samples originating from the target environment but not encompassed within the source environment is denoted as (x t, y). Next, we proceed to alter the distribution measure, taking M (e, v) from Eq. (8) as an illustrative example.
(O, W)
Ea Baeesaeeeeeeeee Ba (XXX)))))))
1[((09 t) + h())tt)
(e,(e')le) [x XX
I[h(a 1) + h(T h(T* 0) 1- + ( (0.
=By(e'lle) [Egewre (x Eg pM xx (x))
[hh(a,, () + h( O1] u.. ().
The third line is a consequence of Hölder's inequality. In the final line, we omit the exponential term ت in = as the function yields results from the set {0, 1}. Similarly, for the term SFe N) V),
I [h(a", t) A + we derive the ultimate bound for the overall R. (h, O v) as shown in Eq. (8).
16

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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
B.3. Proof of Theorem 4.7
In this theorem, we investigate the bounding of distribution risk by empirical risk. The proof employs well-known inequalities such Jensen's inequality, Markov's 's inequality, and Hoeffding's 's inequality. We initially focus on the term S,, 6). The outline of the proof involves utillizing variational inference techniques alter the distribution measure, followed by the application of Markov's 's inequality to compute the risk bound.
Let A (SF. (h, θ)) (h, +) SFe (h, @). By employing the variational inference technique and leveraging Jensen's s inequality, we derive the following inequality:
4(n - 1)²A (SF, (h, 9))²
=4nn - 1)2 (h, 0) - SFe(h, 0))²
22 KL (X (x)) + TX
x
2(n - (X==)
pe (x
[x(x) ((x))
+ Ex exp (2(n - 1)E,. 11 [ (x", t) # yl)
Emenax In exp (2(n I) [1 (x", () + u)))²
(18)
I (2(n 1) KL. (X ((X) ((x)) )) [
-2(n
x In (X | 4(x))
+ In E exp (2(n - 1))
S (2(n 1y KT. (g(x" (())))(p((()) X*))
2(n - 1)EE (p (x (X)) = (x)))|[xx-
+ In Eg =x( exp (2(n - 1) (SF
where A (SF))
IR [A (xx 1) v) T.T [h (2x () + n|1 Recall that Hoeffding's inequality, we get the following
inequality.
P(ajai A (SF) 2 7| - exp(
(19)
Then, denoting the density function of A (SF) as (AFF)))
Pissya-1 (SF)) 2 n7] = 2nn²
+ f dA = e 22mm?
+ f(1) = Amne 2mn7
Then, we get
E (exp (2(n - 1)A
[ (2m
(SF)
4nd (SF) (SF:) exp exp ( exp (2n ())())))))())))))))))) da (SF)
2A (SF)) exp 22 (SF)) d2A (SF)
(20)
ne 2A(SF)) (2A (SF)) +1)
0
< ne (2((FF)
(2A (SF)) +
- 22(5)) (2A (SF) + +1)+n=
=
lim
A
17

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Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
Combining Eq. (20) with Eq. (18), by Markov's inequality, we further get:
Ploya-- A (SF)) 2 1/ S e
Suppose that 17 In(n/e), and with the probability of at least 1 - e, we have that for all xx.,
Eq. (18)
2 (2(n 1)EE KL (1e [(x) (xx))][xxx
2(n 1L (x ((X) (=)))] + In(n/c))*
Then we have
8F (h, 0) - SFo(h, O)
KL (x((X' ((x) (xx))||
1
E, (pe(X"
(X" ((x) +(x)))
+ 2(n (n--) In(n/c)
< Egn KL KL. p% (X" [x(X) (xx))][Txx+
KE,KL (P (x* |x(X) (x))))
(xx
+ 2(n - 1)
In In(n/e)
According to the assumption, we have
(h, - -FF,,,)) 0)
SL (x= ((x) = (xx))][TX=)
1 + 2(n - 1)
In(n/c)+ +
We get the results demonstrated in Theorem 4.7 (1).
Mr ( where ( v Different from Theorem 4.7 (1), the monotonicity measurement has extra expectation on X". We apply Jensen's 's inequality again and then the variational inference trick to get the derivation results.
For the term M (O, (9, V), we define A (M2) B (X
M. v) TI [h (w8, () # h (xx, f ()].
=
Eggn
(M.(O.)) v) M7. w)) 2
4(n - 1 (Mc)² = 4(n - 4(n-1)²
(21)
Then, we consider the term MaO, v and (O, 1) separately.
M v)
Eg E (Xx
# h (x',t)
Ex=Ex in p6 (x
((X) = ((x))
-E,
Ex Ex
x
pd X ((X)= = ((x))
In
(22)
Tx=
x
+Ex=Ex x In (X ((X)
(xx)) P. X
((X) = (2x)
exp (x () # h (0 (())]
((()) KL (p (x ((X) = (x)))|
+KL pe (X" Φ(x) = ([)))][TXX
+ In Eage Exe exp (EEl 1A (xx t) a h (t)
18

---

Invariant Deep Uplift Modeling for Incentive Assignment in Online Marketing
Similarly, for the empirical risk M (0, v):
( W
R (a B (x "0
[b (xx, 1) + h (30 1)]
ExxeXxx In (x
(((X) ((z)))
Eg
+ Ex
xx
Pe (x" ((X)= = (xx))
In
x
(23)
+Ex.Ex x In
TX=
x
pe (x'1 (xX) = (z)) P. (X"
(xX) = (x)))
exp (T (3r" 1) * h (ax, [[]]]
E (a.../e
KL pe (x (xx) = ((x))||TX++
+ KT.
p (X
((X) = ((x))) xx²² ]]
+ In Ems Ex ~ixe exp (E,ll I/ (x=,, 1) # h (T",0)]
Combining Eq. (23) with Eq. (22) and plugin to Eq. (21), we have
4(n - 1)ا2 (Mc)²
= -4n- - 1)² (M,(O, V) - M0, w1)²
I (2(n - 1)
[B (x= (xx) = (x)))|
+ E KL
(pe (x |x(X)= ((xx)||Tx)+
+E. KL p (X")
(xX) = (xx)) |
exp (2(n 1)A (M)))) 3 + In Ege x Ex wit
where A (M²) = (x)) (1), thus we get the theoretical results of Theorem 4.7 (2).
t) - E.I I (z: t) + h (x t)]l The rest of the proof is similar to Theorem 4.7
19


Reviews:
[{"review_id": "VCiMVVPdwn", "reviewer": "Reviewer_xxdc", "summary": "This paper introduces the IDUM method for predicting uplift in an out-of-distribution setting. It utilizes a Gumbel Softmax-based feature selection mechanism to identify a relevant subset of features, followed by invariant property learning. Additionally, the balancing discrepancy component mitigates selection bias, improving model robustness. Through empirical evaluations, the authors claim that these three components collectively enhance uplift prediction in online marketing.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Dear Reviewer xxdc**,\n\nThank you for taking the time to review our work, we sincerely appreciate your insightful comments, which have helped improve our paper. Below, we provide point-by-point responses to each concern raised.\n\n**Methods And Evaluation Criteria:**\n\nWe will follow your advice to include the the detailed definitions of AUUC and Qini coefficients and revise the presentation in our final version.\n\n\n**Weaknesses:**\n\n**1. Three components are derived from previous research**\n\nOur main contribution is to solve the OOD problem in uplift modeling by introducing the PNS risk, which has been not fully investigated by previous works. \n\nIn our work, we build upon existing methods to construct our model architecture. However, due to differences in application scenarios, additional components are required to address the problem effectively. For OOD uplift modeling, we account for the **in-distribution shift** between treatment and control groups by employing a discrepancy regularizer—a common solution that is not our key contribution. To address the PNS risk, we introduce a novel intervention and prediction procedure for balanced embedding learning, which distinguishes our approach from prior work. However, we observed that the **computational cost** of PNS-based feature optimization was prohibitively high. To mitigate this, we adopted a Gumbel-Softmax-based feature selection mechanism.\n\nThe theoretical foundations of our work are primarily based on Pearl's causal framework, with additional insights adapted from Yang et al. (2024) to enhance rigor. However, our approach is not a direct application of their theorems, but rather a tailored extension for uplift modeling. First, our focus differs fundamentally from Yang et al. (2024): while they address image classification, we tackle uplift estimation with dual prediction heads. These domains differ critically in objectives and assumptions—for instance, uplift modeling requires counterfactual reasoning absent in standard classification. This divergence necessitates theoretical adaptations. Second, we explicitly model the interaction between prediction heads and balanced embeddings within our theoretical framework, which is uniquely designed for our problem setting. Finally, all prior works have been properly cited to maintain academic norms and contextualize our contributions.\n\n**2. Online experiments.**\n\nFollowing your suggestions, we conducted an online experiment to evaluate our proposed IDUM against the baseline CFRNet. Due to the limited time of rebuttal and the cost of algorithm deployment, we only keep it for three days.\n\n**Experimental Setup:**\n\nIn-Distribution (ID) Test: We selected two user groups with similar distributions to the training data.\n\nOut-of-Distribution (OOD) Test: We used two user groups with distinct distributions to assess generalization.\n\n**Evaluation Protocol:**\n\nDue to the constraints of online inference, we could not obtain the true responses for users unaffected by the deployed algorithm. Instead, we compared the watch time improvement across experimental groups as the key metric.\n\n- **Watch time evaluation**\n| Method  | ID    | OOD    |\n|---------|-------|--------|\n| CFRNet  | 0     | 0      |\n| IDUM    | 0.012%| 0.028% |\n\n- **Cost evaluation**\n| Method  | ID    | OOD    |\n|---------|-------|--------|\n| CFRNet  | 0     | 0      |\n| IDUM    | -1.21%| -1.75% |\n\n\nWe report the percentage of watch time improvement relative to CFRNet's performance (baseline, set at 0). And also, we evaluate the cost of two methods, for that we assign less incentives (-1.21% and -1.75%) to the user group and get competitive performance (0.012% and 0.028%).\n\nThe results demonstrate that our proposed IDUM achieves further gains in the OOD testing environment.\n\n\n\n\n**Questions**\n\n\n**1. clarify the settings of the Lazada dataset**\n\nThe Lazada dataset is a public dataset for uplift modeling, which can be found at: https://drive.google.com/file/d/19iSXsbRXJWvuSFHdcLb0Vi9JCP9Fu41s/view\n\nIn the dataset description, there are 86 fields in total, of which 83 are features(f0-f82). We use the column of is_treat as treatment $t$, and the column label as the response $y$.\nUsually, for uplift modeling, $t$ represents whether the user is assigned the discount or coupon, $y$ represents whether the user is converted. \n\n**2. The variance**\n\nWe apologize for the error in reporting the variance. As you pointed out, the variance was incorrectly magnified by a factor of 10. We will correct this in the final version of our paper. Additionally, we plan to release the code, dataset, and training logs upon obtaining permission from our collaborating company, and the variance can be identified in the training logs. Thank you for your careful attention to this issue.\n\nIf you have any further questions to discuss, we are willing to reply as soon as possible.", "claims_and_evidence": "The authors evaluate their proposed methods against baseline models using AUUC, QINI, and KENDALL metrics on two real-world datasets.", "methods_and_evaluation_criteria": "Evaluation criteria:\nIt would be helpful if the authors could include the definitions of AUUC and Qini coefficients used in this work. Typically, Qini coefficients are defined as the difference between AUUC and the area under the curve of a random model, which differs from the authors' description that it \"scales the responses in the control group.\"", "theoretical_claims": "Looks good to me.", "experimental_designs_or_analyses": "Looks good to me.", "relation_to_broader_scientific_literature": "This paper integrates three previous works for application in uplift modeling. The invariant property learning approach is based on Yang et al. (2024) [Invariant Learning via Probability of Sufficient and Necessary Causes], with all definitions, lemmas, properties, and theorems directly drawn from this work. The feature selection mechanism is adapted from Jang et al. (2016) [Categorical Reparameterization with Gumbel-Softmax], while the distribution discrepancy regularizer is based on Shalit et al. (2017) [Estimating Individual Treatment Effect: Generalization Bounds and Algorithms].", "essential_references_not_discussed": "NA", "other_strengths_and_weaknesses": "Strengths:\n- Provides a comprehensive literature review of related works, including uplift modeling and its applications in online marketing.\n- Conducts analysis on real-world datasets to compare the proposed model with baseline methods.\n\nWeaknesses:\n- The work appears to lack novelty, as all three components are derived from previous research. The theoretical framework is entirely based on Yang et al. (2024) [Invariant Learning via Probability of Sufficient and Necessary Causes], and the model optimization objective follows the same paper, with the addition of a distribution discrepancy regularizer.\n- Uplift modeling in online marketing provides better customer targeting strategies. The authors could include an online experiment to justify the proposed methods' effectiveness.", "other_comments_or_suggestions": "None.", "questions_for_authors": "1. Could the authors clarify the settings of the Lazada dataset? Based on my understanding, the treatments in this dataset correspond to different voucher distribution strategies. What is the response variable (i.e., the y values) used in the model?\n2. The proposed IDUM method exhibits an unusually large variance in AUUC on both the ID and OOD Lazada datasets, with a standard error of 0.02, whereas other methods have standard errors around 0.002–0.003. Could the authors investigate and explain the reason for this magnitude difference?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "2ZXyaqNcwV", "reviewer": "Reviewer_UDxr", "summary": "The paper proposes Invariant Deep Uplift Modeling (IDUM) for incentive assignment in online marketing (e.g., coupons or discounts). The model identifies features that are both necessary and sufficient under distribution shifts (e.g., changes in user demographics, time, or geography). It builds on the Probability of Necessity and Sufficiency (PNS) framework from Pearl’s causality theory. A Gumbel-Softmax-based selection layer masks out irrelevant or unstable features, enabling the model to focus on “invariant” causal relationships and reduce computational overhead. It uses an integral probability metric (IPM) to control distributional difference to mitigate selection bias, aligning distributions of treated and control users in a latent representation. The experiment shows that IDUM provides robust uplift prediction under out-of-distribution (OOD) shifts and outperforms multiple baselines.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Dear Reviewer UDxr**,\n\nThank you for taking the time to review our work, we sincerely appreciate your insightful comments, which have helped improve our paper. Below, we provide point-by-point responses to each concern raised.\n\n**Weaknesses:**\n\n\n\n1. **Additional experiments**:\n\nDue to the inherent constraints of our model's design, we are unable to generalize our approach to domains with significantly different characteristics within the rebuttal period. However, in response to your feedback, we have conducted additional experiments on the Criteo dataset (ad click-through rate prediction) to validate our method's ability.\n\nTraining Data: 80% (in-distribution)\n\nID Test Data: 10% (in-distribution)\n\nOOD Test Data: 10% (unbiased sampling)\n\nThis partition allows us to evaluate both in-distribution performance and out-of-distribution generalization.\n\n\n| Method          | ID AUUC           | ID QINI           | ID KENDALL       | OOD AUUC          | OOD QINI          | OOD KENDALL     |\n|-----------------|-------------------|-------------------|------------------|-------------------|-------------------|-----------------|\n| S-Learner       | 0.0973 ± 0.0027   | 0.0356 ± 0.0121   | 0.0091 ± 0.0077  | 0.0939 ± 0.0021   | 0.0361 ± 0.0097   | 0.0093 ± 0.0064 |\n| T-Learner       | 0.1025 ± 0.0022   | 0.0422 ± 0.0109   | 0.0117 ± 0.0063  | 0.0919 ± 0.0022   | 0.0411 ± 0.0115   | 0.0087 ± 0.0068 |\n| TARNet          | 0.1031 ± 0.0024   | 0.0411 ± 0.0145   | 0.0109 ± 0.0037  | 0.0915 ± 0.0023   | 0.0398 ± 0.0127   | 0.0093 ± 0.0072 |\n| CFRNet-mmd      | **0.1042 ± 0.0032** | 0.0429 ± 0.0099   | 0.0112 ± 0.0047  | 0.0924 ± 0.0019   | 0.0339 ± 0.0133   | 0.0109 ± 0.0064 |\n| CFRNet-wass     | 0.0922 ± 0.0022   | 0.0391 ± 0.0110   | 0.0122 ± 0.0051  | 0.0908 ± 0.0024   | 0.0401 ± 0.0117   | 0.0101 ± 0.0039 |\n| DragonNet       | 0.1037 ± 0.0020| 0.0429 ± 0.0127   | 0.0112 ± 0.0044  | 0.1009 ± 0.0021   | 0.0372 ± 0.0130   | 0.0107 ± 0.0048 |\n| EUEN            | 0.1029 ± 0.0031   | 0.0421 ± 0.0118   | 0.0132 ± 0.0050  | 0.1007 ± 0.0029   | 0.0396 ± 0.0134   | 0.0092 ± 0.0061 |\n| UniTE           | 0.1033 ± 0.0036   | 0.0467 ± 0.0137   | 0.0157 ± 0.0049  | 0.0901 ± 0.0027   | 0.0401 ± 0.0125   | 0.0073 ± 0.0057 |\n| TEED            | 0.0923 ± 0.0021   | 0.0436 ± 0.0132 | 0.0127 ± 0.0061  | 0.0902 ± 0.0029   | 0.0335 ± 0.0117   | 0.0092 ± 0.0043 |\n| **IDUM**        | 0.1027 ± 0.0023   | __0.0482 ± 0.0093__   | **0.0163 ± 0.0133**  | **0.1019 ± 0.0023** | **0.0442 ± 0.0105** | **0.0112 ± 0.0054** |\n\n\n2. **Gumble softmax features**:\n\nBoth the Lazada dataset (with over 80 features) and the Production dataset (with over 100 features) exhibit high dimensionality. To address the computational challenges posed by such large feature sets, we employ Gumbel-Softmax-based feature selection, which effectively reduces computational costs while preserving predictive performance.\n\nWhile the Lazada dataset lacks feature interpretability, our analysis of the Production dataset reveals that certain features—such as Phone_type, Region, Silcon, and Age, etc., are consistently retained across selections. This suggests their importance in modeling uplift across diverse scenarios.\n\nIf you have any further questions to discuss, we are willing to reply as soon as possible.", "claims_and_evidence": "All main claims (better uplift prediction, out-of-distribution robustness, correctness of the bounding arguments) appear to be well-supported by both empirical results and theoretical analysis.", "methods_and_evaluation_criteria": "The proposed method (IDUM) makes sense for the problem: it specifically addresses two big challenges in real-world uplift modeling:\n- Selection bias between treated/control groups in observational data.\n- Distribution shift over time or across user populations.\n\nThe evaluation criteria (AUUC, QINI, Kendall) are standard in uplift modeling literature. The chosen real-world datasets cover ID and OOD scenarios, which is a strong design choice to demonstrate generalization capacity although more diverse evaluation dataset could help prove the model can work well under different conditions.\n\nOverall, the methods align well with the practical online marketing setting, and the metrics/datasets are appropriate and standard for uplift tasks.", "theoretical_claims": "The theorical claims mostly from Pearl's existing work and are correct. The claims specific for this paper uses bounding techniques consistent with prior works (e.g union bounds, Jensen's inequality), and the proofs given are coherent, consistent with prior literature, and appear correct under the listed assumptions.", "experimental_designs_or_analyses": "- The experiments compare IDUM to widely used uplift baselines (S-learner, T-learner, TARNet, CFRNet, DragonNet, etc.) using the same training setup, hyperparameter tuning strategies, and standard metrics.\n- Authors test both in-distribution and out-of-distribution performance, which directly addresses the paper’s main claim of robustness to real-world shifts.\n- The ablation studies (removing the balancing discrepancy term, the invariant property learning term, or the feature selection) confirm that each piece meaningfully contributes to performance.", "relation_to_broader_scientific_literature": "The approach is well-situated in the intersection of causal inference, domain adaptation, and uplift modeling.\n- The paper builds on prior works like S-learner, T-learner, TARNet, CFRNet, etc., addressing the standard challenge of biased observational data and distribution mismatch in real systems.\n-  Relates to Pearl’s framework for identifying causal effects under exogeneity and monotonicity. The paper is among the few that directly incorporate “Probability of Necessity and Sufficiency” for robust OOD generalization.\n- Connects to literature on distribution shift (e.g., IRM, domain adversarial training), but specifically tailors these ideas for uplift models in marketing contexts.", "essential_references_not_discussed": "NA", "other_strengths_and_weaknesses": "Strengths\n\n- The paper builds its methodology on Pearl’s causality framework, especially around Probability of Necessity and Sufficiency. This is a clear and principled way to identify robust features for uplift.\n- The authors convincingly motivate the need for out-of-distribution generalization in real-world incentive assignment and illustrate why traditional uplift approaches can fail under changing user distributions.\n-  The paper provides not only an invariant learning approach but also attempts to back it up with a set of domain adaptation–style bounds, which is valuable in a field that often has few formal generalization guarantees.\n\nWeaknesses:\n\n- While the paper does well to include two real-world datasets (Lazada and a short-video platform), these are still both from online platforms. Including more varied or publicly accessible datasets (e.g., from different verticals or domains) could strengthen the claims about broad applicability.\n- Their Gumbel-Softmax–based feature selection is a major part of the proposed approach, yet there is only a limited discussion of which features get included or excluded and why. Additional analysis or interpretability results—especially highlighting which features consistently remain selected—could offer insights into the invariant property learning.", "other_comments_or_suggestions": "Please see the weakness part.", "questions_for_authors": "NA", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ne3I9D2RSj", "reviewer": "Reviewer_4KLk", "summary": "This study addresses uplift modeling for incentive allocation in online markets, aiming to resolve out-of-distribution generalization challenges and selection bias by eliminating spurious correlations. The authors propose the Invariant Deep Uplift Modeling (IDUM) framework, which innovatively integrates a cross-domain invariant learning approach to identify causal features with necessary and sufficient properties. The model employs a Gumbel-Softmax-based feature selection module to enhance computational efficiency and introduces a balanced discrepancy constraint mechanism to mitigate distributional biases between treatment and control groups. Empirical evaluations on real-world commercial datasets (e.g., Lazada) demonstrate that the proposed method significantly outperforms existing benchmarks in response prediction tasks, showcasing superior causal inference capabilities. Overall, the paper exhibits clear motivations, a rigorous theoretical framework, and well-designed experiments with practical implications, all presented with logical coherence and academic rigor.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Dear Reviewer 4KLk**,\n\nThank you for taking the time to review our work, we sincerely appreciate your insightful comments, which have helped improve our paper. Below, we provide point-by-point responses to each concern raised.\n\n**Cons**\n\n1. **Open-source code**: We have included our code in the Supplementary Material for review. Upon acceptance of the paper, we will open-source all code and datasets to ensure reproducibility, and will provide the GitHub link in the final version.\n\n2. **Mathematical formulation**: Additionally, we have added a notation table in the appendix for clarity, and will further expand the explanations in our final revision to enhance understanding.\n\nIf you have any further questions to discuss, we are willing to reply as soon as possible.", "claims_and_evidence": "See summary.", "methods_and_evaluation_criteria": "See summary.", "theoretical_claims": "See summary.", "experimental_designs_or_analyses": "See summary.", "relation_to_broader_scientific_literature": "See summary.", "essential_references_not_discussed": "See summary.", "other_strengths_and_weaknesses": "Pros:\n1. The IDUM framework introduces an improved approach to overcome limitations in handling out-of-distribution (OOD) challenges. Its design consists of three straightforward components: invariant property learning, feature selection, and balancing discrepancy. The method has been carefully developed and supported by mathematical analysis.\n2. Extensive experiments are performed to validate the model's effectiveness. Experiments covered two widely-used benchmark datasets and one real-world industrial dataset, with performance comparisons made against standard reference methods in the field.\n\nCons: \n1. The study currently does not publicly share its implementation code, which limits reproducibility and poses a challenge for independent verification or further development by the research community.\n2. Some technical sections involving mathematical formulations may require simplifications or clearer explanations to improve accessibility for readers with varying levels of expertise.", "other_comments_or_suggestions": "NA", "questions_for_authors": "NA", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "jId5nb9YnL", "reviewer": "Reviewer_UCNa", "summary": "This work investigates uplift modeling for incentive allocation in digital marketplaces, addressing two critical challenges: OOD generalization and selection bias mitigation through spurious correlation elimination. The proposed IDUM framework introduces: 1) A causal invariance learning mechanism identifying domain-agnostic features with necessity and sufficiency properties. 2) A differentiable Gumbel-softmax feature selector for computational efficiency. 3) A distributional discrepancy regularizer aligning treatment-control group representations. Empirical validation on production datasets demonstrates IDUM's superior performance in response prediction compared to existing baselines.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer UCNa,\n\nThank you for taking the time to review our work, we sincerely appreciate your insightful comments, which have helped improve our paper. Below, we provide point-by-point responses to each concern raised.\n\n1. **Mathematical Formulations**: We appreciate the valuable feedback and have incorporated a comprehensive notation table in the appendix to improve clarity. In our final revision, we will further enhance these explanations to ensure better understanding of our methodology.\n\n2. **Computational Complexity Analysis**: We analyze the computational complexity of each module in our framework:\n\n**Invariant Property Learning Module**\n   - Objective loss and negative log-likelihood: $O(n)$ (linear complexity)\n   - KL divergence: $O(n \\times d)$, where $d$ is the feature dimensionality\n\n**Feature Selection Module**\n   - Forward propagation (linear transformation + batch normalization): $O(n \\times h)$, where $h$ is hidden layer dimension\n   - Mask generation (Gumbel-Softmax): $O(k \\times m)$ for $k$ iterations on $m$ mask elements\n   - Total complexity: $O(n \\times h + k \\times m)$\n\n**Discrepancy Balancing Module**\n   - IPM with MMD distance: $O(n^2)$\n\nThe overall time complexity of IDUM is $O(n^2) + O(n \\times h) + O(k \\times m)$.\n\n**Empirical Runtime Comparison**\n\nWe compare the computational efficiency of different methods on two datasets:\n\n| Method         | Production Dataset | Lazada Dataset |\n|----------------|-------------------:|---------------:|\n| S-Learner      | 37 min            | 27 min         |\n| T-Learner      | 40 min            | 28 min         |\n| TARNet         | 58 min            | 49 min         |\n| CFRNet-mmd     | 61 min            | 53 min         |\n| CFRNet-wass    | 122 min           | 117 min        |\n| DragonNet      | 73 min            | 64 min         |\n| EUEN           | 65 min            | 35 min         |\n| UniTE          | 110 min           | 86 min         |\n| TEED           | 93 min            | 89 min         |\n| IDUM (ours)    | 85 min            | 79 min         |\n\nIf you have any further questions to discuss, we are willing to reply as soon as possible.", "claims_and_evidence": "Yes.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "Yes.", "experimental_designs_or_analyses": "Yes.", "relation_to_broader_scientific_literature": "This paper addresses the challenge of testing data that is out-of-distribution.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "**Strengths**\n\nMethodological Innovation: IDUM presents a novel paradigm for uplift modeling under distribution shifts. Its emphasis on causal invariance and feature sufficiency/necessity decomposition addresses critical gaps in real-world deployment scenarios.\n​Theoretical Rigor: The authors establish formal generalization guarantees through β-divergence analysis and PNS risk bounding. The integration of distributional alignment metrics (IPM, MMD) provides principled control of treatment group biases.\nGood narration: The authors skillfully present the main ideas of the article, helping to understand the key counter-attributions.\n\n**Weaknesses**\n\n1. The mathematical formulations underpinning the proposed methodology present certain complexities in comprehension, which could be mitigated through supplementary elucidation to strengthen theoretical transparency.\n2. The work lacks an explicit discussion of the model's computational overhead during training phases and omits details regarding algorithmic complexity analysis. These omissions hinder the practical evaluation of real-world deployment feasibility. Furthermore, the absence of an exhaustive specification of architectural hyperparameters and optimization configurations compromises the reproducibility of experimental results across diverse datasets.", "other_comments_or_suggestions": "No.", "questions_for_authors": "Please see \"Weaknesses\"", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper addresses a practical problem in uplift modeling for online marketing, aiming to tackle out-of-distribution generalization challenges and selection bias by eliminating spurious correlations. Its emphasis on causal invariance and the decomposition of feature sufficiency and necessity helps bridge important gaps in real-world deployment scenarios. While the core concepts are not entirely novel, their application to these scenarios is valuable. Most of the reviewers' concerns were satisfactorily addressed in the rebuttal. However, the authors are encouraged to incorporate the reviewers' suggestions into the final version.
Decision: Accept (spotlight poster)