# Orthogonal Uplift Learning with Permutation-Invariant Representations for Combinatorial Treatments

arXiv: https://arxiv.org/abs/2602.19851 · HTML: https://mlsanity.com/paper/2602.19851/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Builds on (most cited first, 10 of 10)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [Explicit Feature Interaction-aware Uplift Network for Online Marketing](https://mlsanity.com/paper/2306.00315/) (2023)
- [Learning Disentangled Representations for Counterfactual Regression via Mutual Information Minimization](https://mlsanity.com/paper/2206.01022/) (2022)

## Abstract (arXiv)

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