Orthogonal Uplift Learning with Permutation-Invariant Representations for Combinatorial Treatments

Xinyan Su; Jiacan Gao; Mingyuan Ma; Xiao Xu; Xinrui Wan; Tianqi Gu; Enyun Yu; Jiecheng Guo

stat.MEFeb 23, 2026

Orthogonal Uplift Learning with Permutation-Invariant Representations for Combinatorial Treatments

Authors: Xinyan Su, Jiacan Gao, Mingyuan Ma, Xiao Xu, Xinrui Wan, Tianqi Gu, Enyun Yu, Jiecheng Guo,

Organizations: Didi Chuxing, Beijing, China · School of Statistics, East China Normal University, Shanghai, China · School of Mathematics and Statistics, Beijing Jiaotong University, Beijing, China · School of Statistics and Data Science, Shanghai University of Finance and Economics, Shanghai 200433, P.R. China ·

Abstract

We study uplift estimation for combinatorial treatments. Uplift measures the pure incremental causal effect of an intervention (e.g., sending a coupon or a marketing message) on user behavior, modeled as a conditional individual treatment effect. Many real-world interventions are combinatorial: a treatment is a policy that specifies context-dependent action distributions rather than a single atomic label. Although recent work considers structured treatments, most methods rely on categorical or opaque encodings, limiting robustness and generalization to rare or newly deployed policies. We propose an uplift estimation framework that aligns treatment representation with causal semantics. Each policy is represented by the mixture it induces over contextaction components and embedded via a permutation-invariant aggregation. This representation is integrated into an orthogonalized low-rank uplift model, extending Robinson-style decompositions to learned, vector-valued treatments. We show that the resulting estimator is expressive for policy-induced causal effects, orthogonally robust to nuisance estimation errors, and stable under small policy perturbations. Experiments on large-scale randomized platform data demonstrate improved uplift accuracy and stability in long-tailed policy regimes

Figures & tables

Figure 1: Treatment Net: permutation-invariant embedding of combinatorial treatments. A treatment $T$ is observed through its policy specification: for each context $s\in S$ (instantiated here as $\{s_{1},s_{2}\}$ ), the treatment induces a distribution over atomic actions $a\in\mathcal{A}$ (instantiated as $\{a_{0},a_{1},a_{2}\}$ ). The network first learns embeddings for contexts and actions to form atom representations $\phi(s,a)$ . These atoms are then reweighted by policy probabilities and aggregated via a permutation-invariant sum $z(T)$ , ensuring the representation depends only on the induced mixture. Finally, a learnable map produces the treatment embedding $h(T)$ , which is used by the orthogonalized uplift model (left panel) to estimate the causal effect $\tau(x)$ .

Dataset	Global Population ( $\mathcal{D}_{G}$ )				Core Population ( $\mathcal{D}_{C}$ )
Metrics	Treatment 1 ( $T_{1}$ )		Treatment 2 ( $T_{2}$ )		Treatment 1 ( $T_{1}$ )		Treatment 2 ( $T_{2}$ )
Metrics	AUUC $\uparrow$	MAPE $\downarrow$	AUUC $\uparrow$	MAPE $\downarrow$	AUUC $\uparrow$	MAPE $\downarrow$	AUUC $\uparrow$	MAPE $\downarrow$
Panel A: GMV (LTV) Estimation
Random	0.500	–	0.500	–	0.500	–	0.500	–
Causal Forest	0.611	1.000	0.632	1.850	0.536	1.086	0.536	0.836
DESCN	0.514	2.156	0.597	0.977	0.596	1.256	0.591	1.167

Table 1: Combined Estimation Performance. Comparison of AUUC (

\uparrow

) and MAPE (

\downarrow

) for both GMV (Panel A) and Cost (Panel B) estimation tasks. The results are reported across Global (

\mathcal{D}_{G}

) and Core (

\mathcal{D}_{C}

) populations. Best results are bolded .

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Training Config	Test Set: Global ( $\mathcal{D}_{G}$ )				Test Set: Core ( $\mathcal{D}_{C}$ )
		Treatment 1 ( $T_{1}$ )		Treatment 2 ( $T_{2}$ )		Treatment 1 ( $T_{1}$ )		Treatment 2 ( $T_{2}$ )
		AUUC $\uparrow$	MAPE $\downarrow$	AUUC $\uparrow$	MAPE $\downarrow$	AUUC $\uparrow$	MAPE $\downarrow$	AUUC $\uparrow$	MAPE $\downarrow$
Random	—	0.500	—	0.500	—	0.500	—	0.500	—
Causal Forest	$\mathcal{D}_{G}$ ( $n_{tree}{=}300$ )	0.539	0.898	0.542	0.686	0.451	7.075	0.525	0.503
	$\mathcal{D}_{G}$ ( $n_{tree}{=}500$ )	0.575	2.213	0.550	2.917	0.536	1.086	0.536	0.836
	$\mathcal{D}_{G}$ ( $n_{tree}{=}600$ )	0.611	1.000	0.632	1.850	0.483	1.005	0.489	0.979

Appendix

Table 2: Detailed performance evaluation of LTV (GMV) prediction on the June Test Set . The Training Config column specifies the training data source and tree count (

n_{tree}

) for Causal Forest, and the training epoch tuple

(i,j)

for deep learning models (Global, Core).

Model	Training Config	Test Set: Global ( $\mathcal{D}_{G}$ )				Test Set: Core ( $\mathcal{D}_{C}$ )
		Treatment 1 ( $T_{1}$ )		Treatment 2 ( $T_{2}$ )		Treatment 1 ( $T_{1}$ )		Treatment 2 ( $T_{2}$ )
		AUUC $\uparrow$	MAPE $\downarrow$	AUUC $\uparrow$	MAPE $\downarrow$	AUUC $\uparrow$	MAPE $\downarrow$	AUUC $\uparrow$	MAPE $\downarrow$
Random	—	0.500	—	0.500	—	0.500	—	0.500	—
Causal Forest	$\mathcal{D}_{G}$ ( $n_{tree}{=}300$ )	0.440	0.971	0.412	0.962	0.576	0.946	0.596	0.969
	$\mathcal{D}_{G}$ ( $n_{tree}{=}500$ )	0.692	0.792	0.697	0.881	0.550	1.018	0.549	0.993
	$\mathcal{D}_{G}$ ( $n_{tree}{=}600$ )	0.701	0.954	0.707	0.916	0.566	0.994	0.498	0.999

Appendix

Table 3: Detailed performance evaluation of Cost prediction on the June Test Set . The Training Config column specifies the training data source and tree count (

n_{tree}

) for Causal Forest, and the training epoch tuple

(i,j)

for deep learning models (Global, Core).

Uplift Modeling

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A Large-Scale Empirical Comparison of Meta-Learners and Causal Forests for Heterogeneous Treatment Effect Estimation in Marketing Uplift Modeling

Estimating Conditional Average Treatment Effects (CATE) at the individual level is central to precision marketing, yet systematic benchmarking of uplift modeling methods at industrial scale remains limited. We present UpliftBench, an empirical evaluation of four CATE estimators: S-Learner, T-Learner, X-Learner (all with LightGBM base learners), and Causal Forest (EconML), applied to the Criteo Uplift v2.1 dataset comprising 13.98 million customer records. The near-random treatment assignment (propensity AUC = 0.509) provides strong internal validity for causal estimation. Evaluated via Qini coefficient and cumulative gain curves, the S-Learner achieves the highest Qini score of 0.376, with the top 20% of customers ranked by predicted CATE capturing 77.7% of all incremental conversions, a 3.9x improvement over random targeting. SHAP analysis identifies f8 as the dominant heterogeneous treatment effect (HTE) driver among the 12 anonymized covariates. Causal Forest uncertainty quantification reveals that 1.9% of customers are confident persuadables (lower 95% CI > 0) and 0.1% are confident sleeping dogs (upper 95% CI < 0). Our results provide practitioners with evidence-based guidance on method selection for large-scale uplift modeling pipelines.

Aman Singh

Uplift Modeling Conditional Average Treatment Effect Estimation Causal Effect Estimation

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Aug 2, 2026

UpliftBench: Revealing Outcome-Regime and Objective Mismatch in Uplift Evaluation

Uplift modeling (conditional-average-treatment-effect estimation) drives personalized targeting, yet published uplift benchmarks frequently disagree on which estimator performs best; we show the disagreement is substantially about metrics, not models. UpliftBench evaluates 12 uplift estimators under an outer-test-isolated, multi-objective protocol across seven dataset families; its two findings are identified where a reference objective exists -- F1 on the standard continuous benchmark (IHDP), F2 in a within-sample case study on Jobs. On that benchmark, Qini shows no detectable alignment with effect accuracy -- across all 100 IHDP realizations its mean rank correlation with effect accuracy is +0.07, 95% CI [-0.03, +0.16] -- while AUUC is consistently more aligned (paired prefix-mean-AUUC-over-Qini gap +0.49 [+0.40, +0.59]; the shipped cumulative-gain AUUC aligns better still, +0.73). On Jobs, ranking metrics are structurally insufficient for a sign-threshold policy because they discard the score level; empirically, within the released split-rotation analysis direct policy-risk selection yields lower benchmark regret than random model selection while Qini, AUUC, and uplift-at-

k

do not (14-15% regret). Calibrating the decision threshold removes 81% of the Qini-selection regret. Both findings are bounded, not universal: F1 is not detected on either validation family (the ACIC and Revenue-Synthetic gaps are both indistinguishable from zero), and F2 vanishes under a budgeted-value objective where rank suffices. UpliftBench releases versioned loaders, fixed protocols, result artifacts, and a reproducible living leaderboard; the public repository accompanies the paper.

Binshuang Li

Independent Researcher USA

Conditional Average Treatment Effect Estimation Benchmark Design Policy Evaluation Uplift Modeling Benchmark Validity Individualized Treatment Effect Estimation

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Jul 30, 2026

Multi-channel Uplift Policy Learning

E-commerce platforms must allocate fixed marketing budgets across multiple channels to maximize business utility. However, standard predict-then-optimize (PTO) paradigms fail in this compositional space due to observational confounding and severe extrapolation. We formulate this challenge as a simplex-constrained uplift decision problem and propose ReAlloc, a fast-slow causal framework. Specifically, an agile Orthogonal Teacher extracts unbiased local gradients from short-term logs, while an Explanation-Guided Student distills them into a structured marginal field over long-term horizons. This design enables support-aware, conservative decisions that capture cross-channel substitutions. Extensive simulations and large-scale online A/B tests on Taobao platform demonstrate that ReAlloc achieves simultaneous lifts in both pay order and income.

Changjian Liu, Tianyu Wang, Xiaoxuan Deng +7

Peking University Beijing, China · Alibaba Group Beijing, China · Beihang University Beijing, China +1

Online Resource Allocation

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