# B-Learner: Quasi-Oracle Bounds on Heterogeneous Causal Effects Under Hidden Confounding

arXiv: https://arxiv.org/abs/2304.10577 · HTML: https://mlsanity.com/paper/2304.10577/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 20 Apr 2023.

## Builds on (most cited first, 14 of 14)

- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021)
- [Bounds on the conditional and average treatment effect with unobserved confounding factors](https://mlsanity.com/paper/1808.09521/) (2018)
- [Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing](https://mlsanity.com/paper/2102.04543/) (2021)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [Long Story Short: Omitted Variable Bias in Causal Machine Learning](https://mlsanity.com/paper/2112.13398/) (2021)
- [Robust and Agnostic Learning of Conditional Distributional Treatment Effects](https://mlsanity.com/paper/2205.11486/) (2022)
- [Treatment Effect Risk: Bounds and Inference](https://mlsanity.com/paper/2201.05893/) (2022)
- [Causal effect on a target population: a sensitivity analysis to handle missing covariates](https://mlsanity.com/paper/2105.06435/) (2021)

## Built on by (most cited first, 28 of 28)

- [Causal machine learning for predicting treatment outcomes](https://mlsanity.com/paper/2410.08770/) (2024)
- [Bayesian Neural Controlled Differential Equations for Treatment Effect Estimation](https://mlsanity.com/paper/2310.17463/) (2023)
- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation](https://mlsanity.com/paper/2311.11321/) (2023)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments](https://mlsanity.com/paper/2406.02464/) (2024)
- [Causal Fairness under Unobserved Confounding: A Neural Sensitivity Framework](https://mlsanity.com/paper/2311.18460/) (2023)
- [IGC-Net for conditional average potential outcome estimation over time](https://mlsanity.com/paper/2405.21012/) (2024)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2505.13072/) (2025)
- [Hidden yet quantifiable: A lower bound for confounding strength using randomized trials](https://mlsanity.com/paper/2312.03871/) (2023)
- [Delphic Offline Reinforcement Learning under Nonidentifiable Hidden Confounding](https://mlsanity.com/paper/2306.01157/) (2023)
- [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024)
- [Efficient and Sharp Off-Policy Learning under Unobserved Confounding](https://mlsanity.com/paper/2502.13022/) (2025)
- [Differentially Private Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2503.03486/) (2025)
- [Efficient and Sharp Off-Policy Evaluation in Robust Markov Decision Processes](https://mlsanity.com/paper/2404.00099/) (2024)
- [Generalization Bounds for Causal Regression: Insights, Guarantees and Sensitivity Analysis](https://mlsanity.com/paper/2405.09516/) (2024)
- [Spatial Deconfounder: Interference-Aware Deconfounding for Spatial Causal Inference](https://mlsanity.com/paper/2510.08762/) (2025)
- [Amortizing Causal Sensitivity Analysis via Prior Data-Fitted Networks](https://mlsanity.com/paper/2605.10590/) (2026)
- [Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data](https://mlsanity.com/paper/2406.06452/) (2024)
- [Information-Theoretic Causal Bounds under Unmeasured Confounding](https://mlsanity.com/paper/2601.17160/) (2026)
- [Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring](https://mlsanity.com/paper/2510.13397/) (2025)
- [Causal Inference on Networks under Misspecified Exposure Mappings: A Partial Identification Framework](https://mlsanity.com/paper/2602.03459/) (2026)
- [Neural Networks with Causal Graph Constraints: A New Approach for Treatment Effects Estimation](https://mlsanity.com/paper/2404.12238/) (2024)
- [Conditional Average Treatment Effect Estimation Under Hidden Confounders](https://mlsanity.com/paper/2506.12304/) (2025)
- [Treatment Effect Estimation with Differentiated Networked Effect on Graph Data](https://mlsanity.com/paper/2605.24358/) (2026)
- [What You Observe Determines How You Identify Causal Effects: Evaluating Causal Models across Observational Views](https://mlsanity.com/paper/2609.36881/) (2026)

## Abstract (arXiv)

Estimating heterogeneous treatment effects from observational data is a crucial task across many fields, helping policy and decision-makers take better actions. There has been recent progress on robust and efficient methods for estimating the conditional average treatment effect (CATE) function, but these methods often do not take into account the risk of hidden confounding, which could arbitrarily and unknowingly bias any causal estimate based on observational data. We propose a meta-learner called the B-Learner, which can efficiently learn sharp bounds on the CATE function under limits on the level of hidden confounding. We derive the B-Learner by adapting recent results for sharp and valid bounds of the average treatment effect (Dorn et al., 2021) into the framework given by Kallus & Oprescu (2023) for robust and model-agnostic learning of conditional distributional treatment effects. The B-Learner can use any function estimator such as random forests and deep neural networks, and we prove its estimates are valid, sharp, efficient, and have a quasi-oracle property with respect to the constituent estimators under more general conditions than existing methods. Semi-synthetic experimental comparisons validate the theoretical findings, and we use real-world data to demonstrate how the method might be used in practice.