Direct Profit Estimation Using Uplift Modeling under Clustered Network Interference

Bram van den Akker

REVIEW 4 major objections 5 minor 10 references

Direct Profit Estimation Using Uplift Modeling under Clustered Network Interference

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Promotion policies can be trained directly on incremental profit under clustered interference by using the AddIPW estimator as a differentiable objective.

desk verdict Useful, honest workshop paper that turns AddIPW into a practical profit objective, but its main simulation comparison is confounded by a change of learning criterion. read the letter →

arxiv 2509.01558 v1 pith:GWXIVUOJ submitted 2025-09-01 cs.LG

Bram van den Akker This is my paper · ORCID

classification cs.LG

keywords upliftmodelingclusterednetworkinterferenceAddIPWincrementalprofitresponsetransformationQinicurvespolicylearningpromotionoptimization

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Standard uplift modeling assumes that discounting one item does not affect how other items perform, but in real marketplaces promotions cannibalize each other. This paper proposes training uplift policies that account for such clustered network interference by turning the AddIPW policy estimator into a differentiable objective. The key move is a response transformation that uses each cluster's total outcome rather than the individual item's outcome, so the learned score reflects a treatment's full effect within the group. In simulations, this interference-aware objective outperforms naive uplift baselines, and the gap grows with cluster size; adapting a profit-per-conversion transformation yields the best identification of high-profit interventions at low budgets.

What carries the argument

The load-bearing object is the AddIPW estimator (Additive Inverse Propensity Weighting, a policy-value estimator whose weights grow linearly in cluster size) combined with the response transformation in Eq. 6. That transformation defines a per-unit target Z_ij as the cluster-level outcome Y_i reweighted by inverse propensity, positive for treated units and negative for untreated. Training a differentiable score f_theta to maximize the inner product with Z_ij is shown to be equivalent to maximizing the AddIPW policy value; the cluster-level outcome is what converts a per-item uplift score into a policy that internalizes network interference.

What would settle it

Run the same comparison on a large randomized promotion experiment with known user-session clusters: if an AddIPW-IPC policy does not beat an interference-naive IPC policy on incremental profit per the Qini curve when sessions contain many items, the central claim fails. A cheaper check is in the same simulator: lower the softmax temperature to a value with weak interference and observe whether the AddIPW advantage shrinks or reverses, as the paper's preliminary experiments suggest.

Watch

Extended reading notes

Core claim

Under the additive outcome model, maximizing the sum over clusters and units of Z_ij times a differentiable score f_theta(X_ij), with Z_ij equal to the cluster-level outcome Y_i divided by the propensity for treated units and minus that ratio for untreated units, is equivalent to maximizing the policy-dependent AddIPW objective. The paper's central move is to put the cluster-level average outcome Y_i into this transformed target, so each item's score carries the total effect of treating it on the whole cluster, including cannibalization. Because f_theta is continuous, the objective supports gradient-based learning, and different economic targets can be inserted by swapping Y_i for cluster re

Load-bearing premise

The empirical result rests on the softmax-exponential-decay simulator being a faithful stand-in for real marketplace interference; at low simulated interference strengths, the author reports that the AddIPW advantage over naive methods does not hold, so if real interference is weak or differently structured, the measured Qini gains may not transfer.

Editorial extensions

If this is right

If the central claim holds, promotion policies in marketplaces can be optimized directly for incremental profit instead of conversion, with learned scores already accounting for cannibalization within user sessions.
The equivalence makes any differentiable model class a candidate interference-aware uplift learner without changing the model, only the training target.
Budget-constrained campaigns should prioritize the AddIPW-IPC variant: the paper finds it outperforms other AddIPW variants when only the top 70% or lower fractions of items are treated.
As cluster size grows, the performance gap over naive methods grows, so the benefit of interference-aware learning is largest in settings with many items per user session.
The framework opens a path to adapt other response transformations by substituting cluster-level outcomes, extending beyond the three variants tested.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

In deployments with weak interference, an adaptive rule that chooses between interference-aware and naive objectives could capture most of the benefit; the paper's preliminary low-temperature results hint that the naive estimator is competitive there, but this switching strategy is not tested.
The equivalence between the transformed objective and AddIPW may extend to continuous treatment doses or multi-action coupons if the inverse propensity weights are replaced by a generalized density ratio, potentially covering discount amount optimization, which the paper does not attempt.
The method's guarantees depend on cluster boundaries being known and correct; if real interference crosses session boundaries, for example a user's budget shared across browsing sessions, cluster-level outcomes would misattribute spillover and bias the learned policy.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: the derivation is clean, the framing is honest, and the paper is useful to practitioners. But the headline empirical claim—AddIPW beats interference-naive methods—is not actually established by these experiments, because the AddIPW variants are trained with a linear policy objective while the 'vanilla' baselines are regression response transformations. That is a real internal-validity threat, and the paper doesn't report enough fitting detail to rule it out.

What is new: the paper adapts AddIPW (Zhang and Imai) into a gradient-based learning objective and plugs cluster-level outcomes into existing response transformations (CRVTW, IPC). The algebra from Eq 1 to Eq 5 is correct, and Eq 6 is a valid reparameterization, not circular. The adaptations are sensible and clearly explained. Credit where due: the author says plainly that the advantage over naive methods vanished at lower softmax temperatures, which is more honest than a lot of workshop papers.

Where it wobbles: first, the stress-test concern is on target. Standard CRVTW/IPC are squared-error regression methods that estimate E[Z|X]. The AddIPW objective is a linear functional of f_theta; its optimum saturates. So when AddIPW-IPC is compared to 'vanilla' IPC, the comparison varies both target (cluster-level vs individual outcome) and loss (linear policy objective vs regression). The growing Qini gap cannot be unambiguously credited to interference correction. The paper does not report model class, loss, or fitting details for baselines, so the reader cannot check. Second, the experiments rest on a simulator co-authored by the author; Figures 1 and 2 have no error bars; Figure 3 has them only for one cluster size; and the advantage is explicitly conditional on interference strength. Third, since this is a workshop note, there is no code release for the new method itself, though the simulator repo is referenced.

Still, the core idea holds: cluster-level outcomes in AddIPW transformations are a practical way to optimize profit under interference. The math is right and the limitations are acknowledged. Who should read it: people building promo-targeting systems in e-commerce/marketplaces, and researchers working on interference-aware uplift. It deserves a serious referee, not a desk reject, but the comparison needs a redo: match the learning criterion across all methods, report error bars, and ideally add a real-data or varied-simulation check. I'd take it to reading group as a discussion piece.

Referee Report

4 major / 5 minor

Summary. The paper proposes using the Additive Inverse Propensity Weighting (AddIPW) estimator as a differentiable policy-learning objective for uplift modeling under clustered network interference. Starting from the AddIPW estimator of Zhang and Imai (Eq. 1), the author isolates the policy-dependent part and arrives at an optimization objective (Eqs. 3-5). A transformed outcome Z_ij is then defined (Eq. 6) so that maximizing sum_ij Z_ij f_theta(X_ij) is equivalent to maximizing the AddIPW policy objective. The paper adapts existing response-transformation methods (CRVTW, IPC, and a naive profit variant) by substituting cluster-level revenue or profit for the individual outcome (Eqs. 7-9). Experiments use the simulator of Karlsson et al. [4] and compare AddIPW-based policies to interference-naive baselines using Qini curves, reporting that advantages grow with cluster size and that an AddIPW-IPC adaptation performs best at low treatment fractions.

Significance. The paper addresses a genuine and timely problem: standard uplift modeling assumes SUTVA, while real marketplaces exhibit interference. The algebraic derivation from Eq. 1 to Eq. 5 is correct, and the equivalence stated around Eq. 6 is a valid reparameterization of the AddIPW objective. The proposed cluster-level response transformations are a useful practical bridge between the interference-aware policy-evaluation literature and established uplift methodology. However, the paper's empirical claim of 'significantly outperforms interference-naive methods' is not yet adequately supported: the experiments vary both the learning objective and the target outcome, the primary figures lack error bars, and the author explicitly notes that the advantage reverses at lower interference strengths. The current evidence is suggestive but not conclusive, even before considering external validity.

major comments (4)

[Section 2.2, Eq. (6)] The statement that maximizing sum_ij Z_ij f_theta(X_ij) is 'training a model to predict Z' conflates linear policy optimization with regression. For any measurable f_theta taking values in [0,1], the maximizer of this linear objective is the saturated policy f_theta = 1 where E[Z|X] > 0 and 0 where E[Z|X] < 0, not a calibrated estimate of E[Z|X]. For a parametric model, the objective behaves like a weighted classification-style loss. This distinction is important for the Qini-curve ranking in Section 3, because ranking by a saturated policy score is not the same as ranking by a regression-based uplift score. Please clarify the role of f_theta and discuss calibration/ranking implications, or add a regression-based variant.
[Section 3, Figures 1-2] The comparison is internally confounded. The AddIPW variants maximize the linear objective sum Z f (Eqs. 6-9), while the 'vanilla' CRVTW, IPC, and Conversion baselines are regression methods that minimize squared error on a response-transformed outcome. Thus the experiments vary two factors at once: the target (cluster-level vs. unit-level outcomes) and the learning criterion (linear policy objective vs. squared-error regression). The growing Qini gap with cluster size cannot be unambiguously attributed to the interference correction. Please add ablation experiments that hold the loss fixed (e.g., train the baselines with the same linear objective on unit-level Z, or train the AddIPW variants with a squared-error loss) and report the model class, loss, and fitting details for all methods.
[Section 3, Figures 1-2] Figures 1 and 2 do not show error bars or confidence intervals, while Figure 3 does. The text claims 'a small yet significant advantage' for AddIPW-IPC, but no significance test or variance estimate is provided for the area-under-Qini comparisons. Please report repeated-seed standard deviations/confidence intervals for all points in the primary figures, or at least for the areas, and state the number of simulation runs.
[Section 3, experiment setup and preliminary experiments] All conclusions rest on the simulator of Karlsson et al. [4], whose data-generating process is not described in this paper; the only parameters given are softmax temperature 5.0 and an 8% discount. The author also states that 'in our preliminary experiments, the AddIPW approach did not universally outperform naive methods at lower softmax temperatures.' This directly limits the abstract's claim that the method 'significantly outperforms interference-naive methods.' Please specify the simulator's outcome model and include the low-temperature results or otherwise characterize the interference regime in which the proposed method is intended to help. This is also important because the simulator is co-authored by the present author, so independent replication or at least a fuller description is needed.

minor comments (5)

[Section 3 / Figures 1-3] The Qini curve and 'area under Qini curve' are used as evaluation metrics but no formal definition is given. Please define the incremental conversion/profit quantities and the area computation, or cite the precise equations from [4].
[Section 2.2] Equation (9) uses Y_c^{T=1,i} without defining the notation; clarify that this is the total treatment cost for converted units in cluster i.
[Throughout] Inconsistent capitalization: 'AddIPW' appears both as 'AddIPW' and 'addIPW'; please standardize.
[Section 2.2] The claim that AddIPW Naive Profit 'is likely to fail' is plausible but not demonstrated. Since the method is reported in the experiments, adding a short explanation of observed behavior would strengthen the argument.
[Section 3] The statement that 'AddIPW-IPC uses far less data compared to the other AddIPW methods' would benefit from a precise statement of how many clusters are dropped and how this affects variance.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the AddIPW response transformation is an explicit reparameterization, and the simulator is a code-reproduced external benchmark despite author overlap.

full rationale

The paper's central derivation—defining Z_ij in Eq. 6 and observing that maximizing sum_ij Z_ij f_theta(X_ij) is equivalent to the AddIPW policy-dependent objective in Eq. 5—is a transparent algebraic identity, not a hidden circularity. The paper explicitly states the equivalence and does not present Eq. 6 as an independent prediction; Z_ij is constructed from the same per-unit AddIPW weights that appear in Eq. 5. This is a valid reparameterization of the objective, not a circular fit. The empirical evaluation uses the simulator from Karlsson et al. [4], which is co-authored by the present author, but that simulator is a published, code-reproduced benchmark with a specified data-generating process, and the proposed method is not fitted to it. Per the review rules, such independent, externally reproducible evidence does not raise the circularity score. The manuscript also honestly notes that the AddIPW advantage did not appear at lower interference strengths. The comparison against 'vanilla' CRVTW/IPC baselines may raise an internal-validity concern because both the loss and the target differ, but that is an experimental-design issue, not a circularity of the derivation. No load-bearing self-citation chain or imported uniqueness theorem is present. Overall, the derivation is self-contained and the claimed equivalence is exact by construction, which is legitimate.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The method itself relies on standard causal assumptions (additive outcomes, clustered interference, correct propensities). The experiments introduce several hand-chosen simulation parameters, most notably the softmax temperature which the paper shows materially changes the conclusions. No new causal entities or mechanisms are postulated.

free parameters (4)

softmax temperature = 5.0
Simulation hyperparameter controlling the strength of interference. The paper observes that at lower temperatures the AddIPW advantage disappears, indicating result sensitivity to this choice.
discount rate = 8%
Treatment magnitude in the simulator; chosen by the authors.
number of samples = 100,000
Simulation dataset size; chosen by the authors.
model class for f_theta
The paper mentions logistic regression or gradient-boosted decision trees but does not specify which was used for the reported results, so reproduction requires an unstated modeling choice.

assumptions (4)

domain assumption Additive outcome model holds for the policy value under clustered interference (from Zhang and Imai [9])
The AddIPW estimator in Eq 1 is unbiased only under this assumption, which the paper inherits without restating or testing.
domain assumption Interference is confined to clusters (SUTVA holds across clusters)
This is the clustered network interference assumption introduced in Section 1 and maintained throughout the derivation.
domain assumption Propensity scores e_j are known or correctly specified
The weights in Eqs 5-9 require the true treatment probabilities; in the simulation they are known, but the paper does not discuss estimation error.
ad hoc to paper The softmax-exponential-decay simulator [4] is a faithful proxy for real-world marketplace interference
All empirical claims are generated from this simulator; if the DGP is unrealistic, the claimed improvements may not generalize.

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Cite this review

Pith. "Pith review of Direct Profit Estimation Using Uplift Modeling under Clustered Network Interference." pith.science (2026). https://pith.science/paper/GWXIVUOJ

@misc{pith2026250901558,
  author       = {Pith},
  title        = {Pith review of: Direct Profit Estimation Using Uplift Modeling under Clustered Network Interference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GWXIVUOJ}},
  note         = {Machine review of arXiv:2509.01558}
}

read the original abstract

Uplift modeling is a key technique for promotion optimization in recommender systems, but standard methods typically fail to account for interference, where treating one item affects the outcomes of others. This violation of the Stable Unit Treatment Value Assumption (SUTVA) leads to suboptimal policies in real-world marketplaces. Recent developments in interference-aware estimators such as Additive Inverse Propensity Weighting (AddIPW) have not found their way into the uplift modeling literature yet, and optimising policies using these estimators is not well-established. This paper proposes a practical methodology to bridge this gap. We use the AddIPW estimator as a differentiable learning objective suitable for gradient-based optimization. We demonstrate how this framework can be integrated with proven response transformation techniques to directly optimize for economic outcomes like incremental profit. Through simulations, we show that our approach significantly outperforms interference-naive methods, especially as interference effects grow. Furthermore, we find that adapting profit-centric uplift strategies within our framework can yield superior performance in identifying the highest-impact interventions, offering a practical path toward more profitable incentive personalization.

Figures

Figures reproduced from arXiv: 2509.01558 by the authors.

**Figure 1.** The Area under the Qini curve, comparing various estimation strategies. As the cluster size (n_items) grows, the advantage of using AddIPW as a weighting strategy increases relative to naive approaches. 0 10 20 30 40 50 Number of Items (n_items) 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 Area under Qini Curve @ 70% (Higher is Better) 1e8 Area under Qini Curve @ 70% vs. Number of Items (Temperature = 5.0, Discount = 8%) Model A… view at source ↗

**Figure 3.** Profit vs. Conversion Qini Curve for models trained [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

10 extracted references · 9 canonical work pages

[4]

Rickard KA Karlsson, Bram van den Akker, Felipe Moraes, Hugo M Proença, and Jesse H Krijthe. 2025. Qini curve estimation under clustered network interference. arXiv preprint arXiv:2502.20097 (2025)

work page arXiv 2025
[1]

Aman Agarwal, Kenta Takatsu, Ivan Zaitsev, and Thorsten Joachims. 2019. A general framework for counterfactual learning-to-rank. InProceedings of the 42nd International ACM SIGIR Conference on Research and Development in Information Retrieval. 5–14

work page 2019
[2]

Robin M Gubela, Stefan Lessmann, and Szymon Jaroszewicz. 2020. Response transformation and profit decomposition for revenue uplift modeling. European Journal of Operational Research 283, 2 (2020), 647–661

work page 2020
[3]

Michael G Hudgens and M Elizabeth Halloran. 2008. Toward causal inference with interference. Journal of the american statistical association 103, 482 (2008), 832–842

work page 2008
[5]

Harrie Oosterhuis and Maarten de Rijke. 2021. Unifying online and counterfactual learning to rank: A novel counterfactual estimator that effectively utilizes online interventions. In Proceedings of the 14th ACM international conference on web search and data mining . 463–471

work page 2021
[6]

Hugo Manuel Proença and Felipe Moraes. 2023. Incremental profit per conversion: a response transformation for uplift modeling in e-commerce promotions. arXiv preprint arXiv:2306.13759 (2023)

work page Pith review arXiv 2023
[7]

Nicholas Radcliffe. 2007. Using control groups to target on predicted lift: Building and assessing uplift model. Direct Marketing Analytics Journal (2007), 14–21

work page 2007
[8]

Donald B Rubin. 1980. Randomization analysis of experimental data: The Fisher randomization test comment. Journal of the American statistical association 75, 371 (1980), 591–593

work page 1980

Show all 10 references

[9]

Yi Zhang and Kosuke Imai. 2023. Individualized policy evaluation and learning under clustered network interference. arXiv preprint arXiv:2311.02467 (2023)

2023 arXiv
[10]

Hao Zhou, Shaoming Li, Guibin Jiang, Jiaqi Zheng, and Dong Wang. 2023. Direct heterogeneous causal learning for resource allocation problems in marketing. In Proceedings of the AAAI Conference on Artificial Intelligence , Vol. 37. 5446–5454. Received 7 August 2025; revised 1 S...

2023

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [4]

Rickard KA Karlsson, Bram van den Akker, Felipe Moraes, Hugo M Proença, and Jesse H Krijthe. 2025. Qini curve estimation under clustered network interference. arXiv preprint arXiv:2502.20097 (2025)

work page arXiv 2025

[2] [1]

Aman Agarwal, Kenta Takatsu, Ivan Zaitsev, and Thorsten Joachims. 2019. A general framework for counterfactual learning-to-rank. InProceedings of the 42nd International ACM SIGIR Conference on Research and Development in Information Retrieval. 5–14

work page 2019

[3] [2]

Robin M Gubela, Stefan Lessmann, and Szymon Jaroszewicz. 2020. Response transformation and profit decomposition for revenue uplift modeling. European Journal of Operational Research 283, 2 (2020), 647–661

work page 2020

[4] [3]

Michael G Hudgens and M Elizabeth Halloran. 2008. Toward causal inference with interference. Journal of the american statistical association 103, 482 (2008), 832–842

work page 2008

[5] [5]

Harrie Oosterhuis and Maarten de Rijke. 2021. Unifying online and counterfactual learning to rank: A novel counterfactual estimator that effectively utilizes online interventions. In Proceedings of the 14th ACM international conference on web search and data mining . 463–471

work page 2021

[6] [6]

Hugo Manuel Proença and Felipe Moraes. 2023. Incremental profit per conversion: a response transformation for uplift modeling in e-commerce promotions. arXiv preprint arXiv:2306.13759 (2023)

work page Pith review arXiv 2023

[7] [7]

Nicholas Radcliffe. 2007. Using control groups to target on predicted lift: Building and assessing uplift model. Direct Marketing Analytics Journal (2007), 14–21

work page 2007

[8] [8]

Donald B Rubin. 1980. Randomization analysis of experimental data: The Fisher randomization test comment. Journal of the American statistical association 75, 371 (1980), 591–593

work page 1980